Answer:
f(x) = 1 /x
Explanation:
We know that
[tex]h(x)=f(g(x))=\frac{1}{x-7}[/tex]and
[tex]g(x)=x-7[/tex]Now, what must be the form of f(x)?
Let us guess.
If we said
[tex]f(x)=\frac{1}{x}[/tex]then what would be f(g(x)) in this case?
To find out we simply replace x with g(x). This gives
[tex]f(g(x))=\frac{1}{g(x)}[/tex][tex]\Rightarrow f(g(x))=\frac{1}{x-7}[/tex]which is exactly the form we are told f(g(x)) take! This means our guess was correct and
[tex]\boxed{f(x)=\frac{1}{x}\text{.}}[/tex]