Question

Given: f(x) = x - 7 and h(x) = 2x + 3

Write the rule for h(f(x)). h(f(x)) = 2x - 11 h(f(x)) = 2x - 7 h(f(x)) = 2x - 4 h(f(x)) = 3x - 4

Answer 1

The correct answer option is h(f(x)) = 2x - 11

Explanation:

We are given two functions:

`f(x) = x-7` and
`h(x) = 2x+3`

and we supposed to find another function which is
`h(f(x))`.

To find
`h(f(x))`, we need to substitute the value of
`f(x)` in the other function i.e.
`h(x)` to get:

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

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

`h(f(x))=2x-14+3`

`h(f(x)) 2x-11`

Therefore, the correct answer is h(f(x)) = 2x - 11.

Answer 2

`h(f(x))=2x-11`

EXPLANATION

Given
`f(x)=x-7`

and

`h(x)=2x+3`

We want to find

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

This means we substitute the function
`f` in to another function
`h` and evaluate.

This implies that;

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

We expand the parenthesis to obtain;

`h(f(x))=2x-14+3`

We simplify further to obtain;

`h(f(x))=2x-11`

Hence the correct answer is A