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Algebra 2 Flashcards: Find And Write An Inverse Function

Study Find And Write An Inverse Function in Algebra 2 with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

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What this deck covers

This deck focuses on Find And Write An Inverse Function, giving you a quick way to review the definitions, rules, and examples that matter most for Algebra 2.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Algebra 2 Flashcards: Find And Write An Inverse Function

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QUESTION

What is the inverse of f(x)=xf(x)=\sqrt{x}f(x)=x​ with domain x≥0x\ge 0x≥0?

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ANSWER

f−1(x)=x2f^{-1}(x)=x^2f−1(x)=x2 with domain x≥0x\ge 0x≥0. Square root and square are inverse operations.

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Flashcard 1: What is the inverse of f(x)=xf(x)=\sqrt{x}f(x)=x​ with domain x≥0x\ge 0x≥0?

Answer: f−1(x)=x2f^{-1}(x)=x^2f−1(x)=x2 with domain x≥0x\ge 0x≥0. Square root and square are inverse operations.

Flashcard 2: What is the inverse of f(x)=xx+1f(x)=\frac{x}{x+1}f(x)=x+1x​ with x≠−1x\neq -1x=−1?

Answer: f−1(x)=x1−xf^{-1}(x)=\frac{x}{1-x}f−1(x)=1−xx​ with x≠1x\neq 1x=1. Cross-multiply and solve for yyy after swapping variables.

Flashcard 3: What is the inverse of f(x)=x+12f(x)=\frac{x+1}{2}f(x)=2x+1​?

Answer: f−1(x)=2x−1f^{-1}(x)=2x-1f−1(x)=2x−1. Multiply by 2, then subtract 1.

Flashcard 4: What is the coordinate relationship between inverse functions on a graph?

Answer: Points (a,b)(a,b)(a,b) on fff become (b,a)(b,a)(b,a) on f−1f^{-1}f−1. Coordinates are reflected across y=xy=xy=x.

Flashcard 5: What is the inverse of f(x)=x−43f(x)=\frac{x-4}{3}f(x)=3x−4​?

Answer: f−1(x)=3x+4f^{-1}(x)=3x+4f−1(x)=3x+4. Multiply by 3, then add 4.

Flashcard 6: What restriction on ccc is needed to solve x+1x−1=c\frac{x+1}{x-1}=cx−1x+1​=c for xxx?

Answer: c≠1c\neq 1c=1. Denominator cannot equal zero in rational function.

Flashcard 7: What is the domain restriction for f(x)=x+1x−1f(x)=\frac{x+1}{x-1}f(x)=x−1x+1​?

Answer: x≠1x\neq 1x=1. Domain excludes values making denominator zero.

Flashcard 8: What is the range restriction for f(x)=x+1x−1f(x)=\frac{x+1}{x-1}f(x)=x−1x+1​?

Answer: y≠1y\neq 1y=1. Range excludes horizontal asymptote value.

Flashcard 9: What is the domain of f−1(x)f^{-1}(x)f−1(x) if f(x)=x+1x−1f(x)=\frac{x+1}{x-1}f(x)=x−1x+1​?

Answer: x≠1x\neq 1x=1. Domain of inverse equals range of original function.

Flashcard 10: What is the range of f−1(x)f^{-1}(x)f−1(x) if f(x)=x+1x−1f(x)=\frac{x+1}{x-1}f(x)=x−1x+1​?

Answer: y≠1y\neq 1y=1. Range of inverse equals domain of original function.

Flashcard 11: What is f−1(x)f^{-1}(x)f−1(x) if f(x)=x+3x−2f(x)=\frac{x+3}{x-2}f(x)=x−2x+3​ with x≠2x\neq 2x=2?

Answer: f−1(x)=2x+3x−1f^{-1}(x)=\frac{2x+3}{x-1}f−1(x)=x−12x+3​ with x≠1x\neq 1x=1. Cross-multiply and solve for yyy after swapping variables.

Flashcard 12: What is f−1(x)f^{-1}(x)f−1(x) if f(x)=x−7x+2f(x)=\frac{x-7}{x+2}f(x)=x+2x−7​ with x≠−2x\neq -2x=−2?

Answer: f−1(x)=2x+71−xf^{-1}(x)=\frac{2x+7}{1-x}f−1(x)=1−x2x+7​ with x≠1x\neq 1x=1. Cross-multiply and solve for yyy after swapping variables.

Flashcard 13: What is the solution for xxx in f(x)=cf(x)=cf(x)=c if f(x)=x+1x−1f(x)=\frac{x+1}{x-1}f(x)=x−1x+1​ and c≠1c\neq 1c=1?

Answer: x=c+1c−1x=\frac{c+1}{c-1}x=c−1c+1​. Cross-multiply and solve for xxx.

Flashcard 14: What is the solution for xxx in f(x)=cf(x)=cf(x)=c if f(x)=x3−4f(x)=x^3-4f(x)=x3−4?

Answer: x=c+43x=\sqrt[3]{c+4}x=3c+4​. Add 4, then take cube root.

Flashcard 15: What is the solution for xxx in f(x)=cf(x)=cf(x)=c if f(x)=1xf(x)=\frac{1}{x}f(x)=x1​ and c≠0c\neq 0c=0?

Answer: x=1cx=\frac{1}{c}x=c1​. Take reciprocal of ccc.

Flashcard 16: What is the solution for xxx in f(x)=cf(x)=cf(x)=c if f(x)=ax+bf(x)=ax+bf(x)=ax+b and a≠0a\neq 0a=0?

Answer: x=c−bax=\frac{c-b}{a}x=ac−b​. Subtract bbb, then divide by aaa.

Flashcard 17: What is the solution for xxx in f(x)=cf(x)=cf(x)=c if f(x)=2x3f(x)=2x^3f(x)=2x3?

Answer: x=c23x=\sqrt[3]{\frac{c}{2}}x=32c​​. Divide ccc by 2, then take cube root.

Flashcard 18: What is the inverse of f(x)=7−4xf(x)=7-4xf(x)=7−4x?

Answer: f−1(x)=7−x4f^{-1}(x)=\frac{7-x}{4}f−1(x)=47−x​. Subtract from 7, then divide by 4.

Flashcard 19: What is the inverse of f(x)=2x3+1f(x)=\frac{2x}{3}+1f(x)=32x​+1?

Answer: f−1(x)=32(x−1)f^{-1}(x)=\frac{3}{2}(x-1)f−1(x)=23​(x−1). Subtract 1, then multiply by 32\frac{3}{2}23​.

Flashcard 20: What is the inverse of f(x)=5−x3f(x)=\frac{5-x}{3}f(x)=35−x​?

Answer: f−1(x)=5−3xf^{-1}(x)=5-3xf−1(x)=5−3x. Subtract from 5, then divide by 3.

Flashcard 21: What is the inverse of f(x)=x−62f(x)=\frac{x-6}{2}f(x)=2x−6​?

Answer: f−1(x)=2x+6f^{-1}(x)=2x+6f−1(x)=2x+6. Multiply by 2, then add 6.

Flashcard 22: What is the inverse of f(x)=(x+2)3−5f(x)=(x+2)^3-5f(x)=(x+2)3−5?

Answer: f−1(x)=x+53−2f^{-1}(x)=\sqrt[3]{x+5}-2f−1(x)=3x+5​−2. Add 5, take cube root, then subtract 2.

Flashcard 23: What is the inverse of f(x)=(x−3)3f(x)=(x-3)^3f(x)=(x−3)3?

Answer: f−1(x)=x3+3f^{-1}(x)=\sqrt[3]{x}+3f−1(x)=3x​+3. Take cube root, then add 3.

Flashcard 24: What is the inverse of f(x)=−2x3+6f(x)=-2x^3+6f(x)=−2x3+6?

Answer: f−1(x)=6−x23f^{-1}(x)=\sqrt[3]{\frac{6-x}{2}}f−1(x)=326−x​​. Subtract from 6, divide by 2, then take cube root.

Flashcard 25: What is the inverse of f(x)=x3−1f(x)=x^3-1f(x)=x3−1?

Answer: f−1(x)=x+13f^{-1}(x)=\sqrt[3]{x+1}f−1(x)=3x+1​. Add 1, then take cube root.

Flashcard 26: What is the inverse of f(x)=4x−12x+5f(x)=\frac{4x-1}{2x+5}f(x)=2x+54x−1​ with x≠−52x\neq -\frac{5}{2}x=−25​?

Answer: f−1(x)=1+5x4−2xf^{-1}(x)=\frac{1+5x}{4-2x}f−1(x)=4−2x1+5x​ with x≠2x\neq 2x=2. Cross-multiply and solve for yyy after swapping variables.

Flashcard 27: What is the inverse of f(x)=x−12x+3f(x)=\frac{x-1}{2x+3}f(x)=2x+3x−1​ with x≠−32x\neq -\frac{3}{2}x=−23​?

Answer: f−1(x)=1+3x1−2xf^{-1}(x)=\frac{1+3x}{1-2x}f−1(x)=1−2x1+3x​ with x≠12x\neq \frac{1}{2}x=21​. Cross-multiply and solve for yyy after swapping variables.

Flashcard 28: What is the inverse of f(x)=3xf(x)=\frac{3}{x}f(x)=x3​ with x≠0x\neq 0x=0?

Answer: f−1(x)=3xf^{-1}(x)=\frac{3}{x}f−1(x)=x3​ with x≠0x\neq 0x=0. Reciprocal function with constant numerator.

Flashcard 29: What is the inverse of f(x)=x+42f(x)=\frac{x+4}{2}f(x)=2x+4​?

Answer: f−1(x)=2x−4f^{-1}(x)=2x-4f−1(x)=2x−4. Multiply by 2, then subtract 4.

Flashcard 30: What is the inverse of f(x)=xx+1f(x)=\frac{x}{x+1}f(x)=x+1x​ with x≠−1x\neq -1x=−1?

Answer: f−1(x)=x1−xf^{-1}(x)=\frac{x}{1-x}f−1(x)=1−xx​ with x≠1x\neq 1x=1. Cross-multiply and solve for yyy after swapping variables.