Question

Functions f and h are invertible functions.2f(x) = 11and h(x) = -4(x – 11)Answer two questions about these functions.Write a simplified expression for f(h(x)) in terms of r.f(h(x)) =Are functions f and h inverses?Choose 1 answer:YesNo

Answer 1

Given:

`f(x)=11-(x)/(4),h(x)=-4(x-11)`

To show the given functions are inverses of each other, they must satisfy the following conditions,

`\begin{gathered} (f\circ h)(x)=x \\ (h\circ g)(x)=x \end{gathered}`

Now,

`\begin{gathered} (f\circ h)(x)=f(h(x)) \\ =f(-4(x-11)) \\ =11-((-4(x-11)))/(4) \\ =11+(x-11) \\ =x \end{gathered}`

And,

`\begin{gathered} (h\circ g)(x)=h(f(x)) \\ =h(11-(x)/(4)) \\ =-4((11-(x)/(4))-11) \\ =-4(11-(x)/(4)-11) \\ =x \end{gathered}`

It shows that the given functions are inverses of each other.

Answer:

`\begin{gathered} f\mleft(h\mleft(x\mright)\mright)=x \\ h(f(x))=x \end{gathered}`

Yes. the given functions are inverses of each other.