Question

I need help to do these composition of functions. I have a photo if needed.f(x)=x-3Find (f×f)(10)

Answer 1

The given function:

f(x) = x - 3

`(f\circ f)\text{ = f(f(x))}`

Substitute x = f(x) in the expression:

`\begin{gathered} (f\circ f)\text{ = f(f(x))} \\ (f\circ f)\text{ =f(x-3)} \\ (f\circ f)\text{ =(x}-3)-3 \\ (f\circ f)\text{ =x}-3-3 \\ (f\circ f)\text{ =x}-6 \end{gathered}`

For

`(f\circ f)(10)`

Substitute x = 10 in the expression of (fof)

`\begin{gathered} (f\circ f)(x)=x-6 \\ (f\circ f)(x)=10-6 \\ (f\circ f)(x)=4 \end{gathered}`

Answer: (fof)(10)