Question

Given: f(x) = x - 7 and h(x) = 2x + 3 Write the rule for f(h(x)). f(h(x)) = 2x - 7 f(h(x)) = 2x - 4 f(h(x)) = 3x - 4 f(h(x)) = 3x - 7

Answer 1

`\bf \begin{cases} f(x) = x - 7\\ h(x) = 2x+3 \end{cases}\qquad \qquad \begin{array}{llll} f(~~h(x)~~) = [h(x)]-7\\\\ f(~~h(x)~~) = [2x+3]-7 \end{array} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill f(~~h(x)~~) =2x-4~\hfill`

Answer 2

The correct option is 2.

Explanation:

The given functions are

`f(x)=x-7`

`h(x)=2x+3`

We need to find the value of f(h(x)).

`f(h(x))=f(2x+3)`
`[\because f(x)=x-7]` .... (1)

Substitute x=(2x+3) in function f(x).

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

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

`f(2x+3)=2x-4`

Now, substitute the value of f(2x+3) in equation (1).

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

Therefore the correct option is 2.