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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

Options for first box are: x, 4x, and 8x Options for second box are: the same as the-example-1

1 Answer

5 votes

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

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