113k views
4 votes
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

User BigMadKev
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.