Question

The function h(x) = 1/x-7 can be expressed in the form f(g(x)), where g(x) = x-7), and f(x) is defined as:f(x) =

Answer 1

f(x) = 1 /x

Step-by-step explanation:

We know that

`h(x)=f(g(x))=(1)/(x-7)`

and

`g(x)=x-7`

Now, what must be the form of f(x)?

Let us guess.

If we said

`f(x)=(1)/(x)`

then what would be f(g(x)) in this case?

To find out we simply replace x with g(x). This gives

`f(g(x))=(1)/(g(x))`
`\Rightarrow f(g(x))=(1)/(x-7)`

which is exactly the form we are told f(g(x)) take! This means our guess was correct and

`\boxed{f(x)=(1)/(x)\text{.}}`