Respuesta :

[tex]\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[/tex]

Answer:

The correct option is 2.

Step-by-step explanation:

The given functions are

[tex]f(x)=x-7[/tex]

[tex]h(x)=2x+3[/tex]

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

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

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

[tex]f(2x+3)=(2x+3)-7[/tex]

[tex]f(2x+3)=2x+3-7[/tex]

[tex]f(2x+3)=2x-4[/tex]

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

[tex]f(h(x))=2x-4[/tex]

Therefore the correct option is 2.