[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.