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)=\frac{1}{4}\sqrt[]{x}$

step 1

Find f(g(x))

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

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))

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

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

$\begin{gathered} y^2=\frac{x}{16} \\ y=\pm\frac{1}{4}\sqrt[\square]{x} \end{gathered}$

Part 3

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