Question

What is the answer to the question and how do i solve?

Answer 1

The given functions are

`\begin{gathered} f(x)=(1)/(x^2) \\ g(x)=e^x \end{gathered}`

To find g(f(x)) means substitute x in g by f

`\begin{gathered} g(f(x))=e^(f(x)) \\ g(f(x))=e^{(1)/(x^2)} \end{gathered}`

To find f(g(0)) means replace x in f by g and substitute x by 0

`\begin{gathered} f(g(x))=(1)/((g(x))^2) \\ f(g(x))=(1)/((e^x)^2) \\ f(g(x))=(1)/(e^(2x)) \end{gathered}`

Substitute x by 0

`\begin{gathered} f(g(0))=(1)/(e^(2(0))) \\ f(g(0))=(1)/(e^0) \\ e^0=1 \\ f(g(0))=(1)/(1) \\ f(g(0))=1 \end{gathered}`