Question

Options for first box are: x, 4x, and 8x Options for second box are: the same as the first Options for third box are: are, are not

Answer 1

we have the functions

`f(x)=16x^2`
`g(x)=(1)/(4)\sqrt[]{x}`

step 1

Find f(g(x))

`f(g(x))=16((1)/(4)\sqrt[]{x})^2`

simplify

`f(g(x))=x`

therefore

Part 1

If x≥0 the value of f(g(x)) is x

step 2

Find g(f(x))

`g(f(x))=(1)/(4)\sqrt[\square]{16x^2}`

simplify

`g(f(x))=x`

therefore

Part 2

If x≥0 the value of g(f(x)) is the same as the first

step 3

Find the inverse of function f(x)

`y=16x^2`

exchange the variables

`x=16y^2`

isolate the variable y

`\begin{gathered} y^2=(x)/(16) \\ y=\pm(1)/(4)\sqrt[\square]{x} \end{gathered}`

Part 3

the functions f(x) and g(x) are inverse functions