Question

Given: f(x) = x- 7 and h(x) = 2x + 3
Write the rule for f(h(xc)).

Answer 1

`f(h(xc)) = 2xc-4`

Explanation:

Given

`f(x) = x - 7`

`h(x) = 2x + 3`

Required

`f(h(xc))`

First, calculate h(xc)

If
`h(x) = 2x + 3`

Then

`h(xc) = 2xc + 3`

Solving further:

`f(x) = x - 7`

Substitute h(xc) for x

`f(h(xc)) = h(xc) - 7`

Substitute
`h(xc) = 2xc + 3`

`f(h(xc)) = 2xc + 3 - 7`

`f(h(xc)) = 2xc-4`