Find and Write an Inverse Function - Algebra 2
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What is the inverse of $f(x)=\sqrt{x}$ with domain $x\ge 0$?
What is the inverse of $f(x)=\sqrt{x}$ with domain $x\ge 0$?
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$f^{-1}(x)=x^2$ with domain $x\ge 0$. Square root and square are inverse operations.
$f^{-1}(x)=x^2$ with domain $x\ge 0$. Square root and square are inverse operations.
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What is the inverse of $f(x)=\frac{x}{x+1}$ with $x\neq -1$?
What is the inverse of $f(x)=\frac{x}{x+1}$ with $x\neq -1$?
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$f^{-1}(x)=\frac{x}{1-x}$ with $x\neq 1$. Cross-multiply and solve for $y$ after swapping variables.
$f^{-1}(x)=\frac{x}{1-x}$ with $x\neq 1$. Cross-multiply and solve for $y$ after swapping variables.
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What is the inverse of $f(x)=\frac{x+1}{2}$?
What is the inverse of $f(x)=\frac{x+1}{2}$?
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$f^{-1}(x)=2x-1$. Multiply by 2, then subtract 1.
$f^{-1}(x)=2x-1$. Multiply by 2, then subtract 1.
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What is the coordinate relationship between inverse functions on a graph?
What is the coordinate relationship between inverse functions on a graph?
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Points $(a,b)$ on $f$ become $(b,a)$ on $f^{-1}$. Coordinates are reflected across $y=x$.
Points $(a,b)$ on $f$ become $(b,a)$ on $f^{-1}$. Coordinates are reflected across $y=x$.
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What is the inverse of $f(x)=\frac{x-4}{3}$?
What is the inverse of $f(x)=\frac{x-4}{3}$?
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$f^{-1}(x)=3x+4$. Multiply by 3, then add 4.
$f^{-1}(x)=3x+4$. Multiply by 3, then add 4.
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What restriction on $c$ is needed to solve $\frac{x+1}{x-1}=c$ for $x$?
What restriction on $c$ is needed to solve $\frac{x+1}{x-1}=c$ for $x$?
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$c\neq 1$. Denominator cannot equal zero in rational function.
$c\neq 1$. Denominator cannot equal zero in rational function.
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What is the domain restriction for $f(x)=\frac{x+1}{x-1}$?
What is the domain restriction for $f(x)=\frac{x+1}{x-1}$?
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$x\neq 1$. Domain excludes values making denominator zero.
$x\neq 1$. Domain excludes values making denominator zero.
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What is the range restriction for $f(x)=\frac{x+1}{x-1}$?
What is the range restriction for $f(x)=\frac{x+1}{x-1}$?
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$y\neq 1$. Range excludes horizontal asymptote value.
$y\neq 1$. Range excludes horizontal asymptote value.
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What is the domain of $f^{-1}(x)$ if $f(x)=\frac{x+1}{x-1}$?
What is the domain of $f^{-1}(x)$ if $f(x)=\frac{x+1}{x-1}$?
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$x\neq 1$. Domain of inverse equals range of original function.
$x\neq 1$. Domain of inverse equals range of original function.
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What is the range of $f^{-1}(x)$ if $f(x)=\frac{x+1}{x-1}$?
What is the range of $f^{-1}(x)$ if $f(x)=\frac{x+1}{x-1}$?
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$y\neq 1$. Range of inverse equals domain of original function.
$y\neq 1$. Range of inverse equals domain of original function.
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What is $f^{-1}(x)$ if $f(x)=\frac{x+3}{x-2}$ with $x\neq 2$?
What is $f^{-1}(x)$ if $f(x)=\frac{x+3}{x-2}$ with $x\neq 2$?
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$f^{-1}(x)=\frac{2x+3}{x-1}$ with $x\neq 1$. Cross-multiply and solve for $y$ after swapping variables.
$f^{-1}(x)=\frac{2x+3}{x-1}$ with $x\neq 1$. Cross-multiply and solve for $y$ after swapping variables.
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What is $f^{-1}(x)$ if $f(x)=\frac{x-7}{x+2}$ with $x\neq -2$?
What is $f^{-1}(x)$ if $f(x)=\frac{x-7}{x+2}$ with $x\neq -2$?
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$f^{-1}(x)=\frac{2x+7}{1-x}$ with $x\neq 1$. Cross-multiply and solve for $y$ after swapping variables.
$f^{-1}(x)=\frac{2x+7}{1-x}$ with $x\neq 1$. Cross-multiply and solve for $y$ after swapping variables.
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What is the solution for $x$ in $f(x)=c$ if $f(x)=\frac{x+1}{x-1}$ and $c\neq 1$?
What is the solution for $x$ in $f(x)=c$ if $f(x)=\frac{x+1}{x-1}$ and $c\neq 1$?
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$x=\frac{c+1}{c-1}$. Cross-multiply and solve for $x$.
$x=\frac{c+1}{c-1}$. Cross-multiply and solve for $x$.
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What is the solution for $x$ in $f(x)=c$ if $f(x)=x^3-4$?
What is the solution for $x$ in $f(x)=c$ if $f(x)=x^3-4$?
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$x=\sqrt[3]{c+4}$. Add 4, then take cube root.
$x=\sqrt[3]{c+4}$. Add 4, then take cube root.
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What is the solution for $x$ in $f(x)=c$ if $f(x)=\frac{1}{x}$ and $c\neq 0$?
What is the solution for $x$ in $f(x)=c$ if $f(x)=\frac{1}{x}$ and $c\neq 0$?
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$x=\frac{1}{c}$. Take reciprocal of $c$.
$x=\frac{1}{c}$. Take reciprocal of $c$.
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What is the solution for $x$ in $f(x)=c$ if $f(x)=ax+b$ and $a\neq 0$?
What is the solution for $x$ in $f(x)=c$ if $f(x)=ax+b$ and $a\neq 0$?
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$x=\frac{c-b}{a}$. Subtract $b$, then divide by $a$.
$x=\frac{c-b}{a}$. Subtract $b$, then divide by $a$.
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What is the solution for $x$ in $f(x)=c$ if $f(x)=2x^3$?
What is the solution for $x$ in $f(x)=c$ if $f(x)=2x^3$?
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$x=\sqrt[3]{\frac{c}{2}}$. Divide $c$ by 2, then take cube root.
$x=\sqrt[3]{\frac{c}{2}}$. Divide $c$ by 2, then take cube root.
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What is the inverse of $f(x)=7-4x$?
What is the inverse of $f(x)=7-4x$?
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$f^{-1}(x)=\frac{7-x}{4}$. Subtract from 7, then divide by 4.
$f^{-1}(x)=\frac{7-x}{4}$. Subtract from 7, then divide by 4.
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What is the inverse of $f(x)=\frac{2x}{3}+1$?
What is the inverse of $f(x)=\frac{2x}{3}+1$?
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$f^{-1}(x)=\frac{3}{2}(x-1)$. Subtract 1, then multiply by $\frac{3}{2}$.
$f^{-1}(x)=\frac{3}{2}(x-1)$. Subtract 1, then multiply by $\frac{3}{2}$.
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What is the inverse of $f(x)=\frac{5-x}{3}$?
What is the inverse of $f(x)=\frac{5-x}{3}$?
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$f^{-1}(x)=5-3x$. Subtract from 5, then divide by 3.
$f^{-1}(x)=5-3x$. Subtract from 5, then divide by 3.
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What is the inverse of $f(x)=\frac{x-6}{2}$?
What is the inverse of $f(x)=\frac{x-6}{2}$?
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$f^{-1}(x)=2x+6$. Multiply by 2, then add 6.
$f^{-1}(x)=2x+6$. Multiply by 2, then add 6.
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What is the inverse of $f(x)=(x+2)^3-5$?
What is the inverse of $f(x)=(x+2)^3-5$?
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$f^{-1}(x)=\sqrt[3]{x+5}-2$. Add 5, take cube root, then subtract 2.
$f^{-1}(x)=\sqrt[3]{x+5}-2$. Add 5, take cube root, then subtract 2.
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What is the inverse of $f(x)=(x-3)^3$?
What is the inverse of $f(x)=(x-3)^3$?
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$f^{-1}(x)=\sqrt[3]{x}+3$. Take cube root, then add 3.
$f^{-1}(x)=\sqrt[3]{x}+3$. Take cube root, then add 3.
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What is the inverse of $f(x)=-2x^3+6$?
What is the inverse of $f(x)=-2x^3+6$?
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$f^{-1}(x)=\sqrt[3]{\frac{6-x}{2}}$. Subtract from 6, divide by 2, then take cube root.
$f^{-1}(x)=\sqrt[3]{\frac{6-x}{2}}$. Subtract from 6, divide by 2, then take cube root.
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What is the inverse of $f(x)=x^3-1$?
What is the inverse of $f(x)=x^3-1$?
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$f^{-1}(x)=\sqrt[3]{x+1}$. Add 1, then take cube root.
$f^{-1}(x)=\sqrt[3]{x+1}$. Add 1, then take cube root.
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What is the inverse of $f(x)=\frac{4x-1}{2x+5}$ with $x\neq -\frac{5}{2}$?
What is the inverse of $f(x)=\frac{4x-1}{2x+5}$ with $x\neq -\frac{5}{2}$?
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$f^{-1}(x)=\frac{1+5x}{4-2x}$ with $x\neq 2$. Cross-multiply and solve for $y$ after swapping variables.
$f^{-1}(x)=\frac{1+5x}{4-2x}$ with $x\neq 2$. Cross-multiply and solve for $y$ after swapping variables.
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What is the inverse of $f(x)=\frac{x-1}{2x+3}$ with $x\neq -\frac{3}{2}$?
What is the inverse of $f(x)=\frac{x-1}{2x+3}$ with $x\neq -\frac{3}{2}$?
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$f^{-1}(x)=\frac{1+3x}{1-2x}$ with $x\neq \frac{1}{2}$. Cross-multiply and solve for $y$ after swapping variables.
$f^{-1}(x)=\frac{1+3x}{1-2x}$ with $x\neq \frac{1}{2}$. Cross-multiply and solve for $y$ after swapping variables.
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What is the inverse of $f(x)=\frac{3}{x}$ with $x\neq 0$?
What is the inverse of $f(x)=\frac{3}{x}$ with $x\neq 0$?
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$f^{-1}(x)=\frac{3}{x}$ with $x\neq 0$. Reciprocal function with constant numerator.
$f^{-1}(x)=\frac{3}{x}$ with $x\neq 0$. Reciprocal function with constant numerator.
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What is the inverse of $f(x)=\frac{x+4}{2}$?
What is the inverse of $f(x)=\frac{x+4}{2}$?
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$f^{-1}(x)=2x-4$. Multiply by 2, then subtract 4.
$f^{-1}(x)=2x-4$. Multiply by 2, then subtract 4.
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What is the inverse of $f(x)=\frac{x}{x+1}$ with $x\neq -1$?
What is the inverse of $f(x)=\frac{x}{x+1}$ with $x\neq -1$?
Tap to reveal answer
$f^{-1}(x)=\frac{x}{1-x}$ with $x\neq 1$. Cross-multiply and solve for $y$ after swapping variables.
$f^{-1}(x)=\frac{x}{1-x}$ with $x\neq 1$. Cross-multiply and solve for $y$ after swapping variables.
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