Function Notation

Help Questions

Algebra II › Function Notation

Questions 1 - 10

1

If and , what is $g(f(x))\cdot f(x)$ ?

$\textup{The answer is not given.}$

Explanation

Evaluate first. Substitute the function into .

Distribute the integer through the binomial and simplify the equation.

Multiply this expression with .

The answer is:

2

If and , determine:

Explanation

Substitute the assigned values into the expression.

Simplify the inside parentheses.

The answer is:

3

Find for the following function:

$cos(5g^2+10gh+5h^2)e^{g+h}$

$cos(5g^2+5h^2)e^{g+h}$

$cos(5g^2+10gh+5h^2)e^{g}+e^h$

$cos(5g^2)e^{g}+cos(5h^2)e^{h}$

$cos(5g^2e^{g})+cos(5h^2e^{h})$

Explanation

To find , all we do is plug in wherever we see an in the function. We have to be sure we keep the parentheses. In this case, when we plug in , we get

$cos(5(g+h)^2)e^{g+h}$

Then, when we expand our binomial squared and distribute the , we get

$cos(5g^2+10gh+5h^2)e^{g+h}$

4

If and , what is $a^b\times b^a$

$-\frac{1}{2}$

$-\frac{1}{4}$

Explanation

Substitute the assigned values into the expression.

$(-1)^{(-2)}\times (-2)^{(-1)}$

Simplify the negative exponents by rewriting both terms as fractions.

$x^{-a} =\frac{1}{x^a}$

$(-1)^{(-2)}\times (-2)^{(-1)}= \frac{1}{(-1)^2} \times \frac{1}{(-2)^{1}}$

Simplify the fractions.

$1\times \frac{1}{-2} = -\frac{1}{2}$

The answer is: $-\frac{1}{2}$

5

Evaluate $g(f(\frac{1}{95}))$ if: and $f(x) = \frac{1}{95}$

$\frac{1}{95}$

$\frac{1}{9025}$

Explanation

Evaluate $g(f(\frac{1}{95}))$ by solving for $f(\frac{1}{95})$ first.

No matter what value of , $f(x) = \frac{1}{95}$ . This means that:

$f( \frac{1}{95}) = \frac{1}{95}$

Then:

$g(\frac{1}{95})$

For any value of , . This means that:

$g(\frac{1}{95}) = 95$

The answer is:

6

Given the function , what is the value of ?

Explanation

Substitute negative three into the function.

Simplify this equation by order of operations.

The answer is:

7

What is the value of if and ?

Explanation

Substitute the assigned values into the expression.

Simplify by order of operations.

The answer is:

8

Given the function: , what is ?

Explanation

To solve this function, the term means to replace negative four with the x-variable.

Use order of operations and simplify the terms on the right side.

The answer is:

9

Evaluate if and

Explanation

Substitute the known values into the expression.

Simplify the expression.

The answer is:

10

Determine if and .

Explanation

Substitute three into the function of to solve for .

Substitute this value into the function .

There is no x-variable to substitute nine, which means the function is equal to three.

The answer is:

Page 1 of 5

Return to subject