Question

Find the component g.

Given the function
f(x)= x - 2
-------
5
gf(x) = x - 3

How to solve this question? Can you show me how to do it step by step?

Answer 1

The function
`g(x) = x-1`

Explanation:

Here
`f(x) = x-2`

Let
`y=x-2`

Solving for x we get

`x=y+2` ....(1)

We are also given that

`g(f(x)) = x-3`

So we replace
`f(x) \ by \ y`

We get

`g(y) = x-3`

But
`x=y+2 \ from \ (1)`

We have

`g(y) = y+2-3`

`g(y)=y-1`

or

`g(x)=x-1`