Question

If h(x)=(f o g)(x) and h(x)= 4sqrt x+7, find g(x) if f(x)= 4sqrt x+1

Answer 1

Answer:
`g(x)= x+6`

Explanation:

Given functions are:
`f(x)= 4√(x+1)` and
`h(x)= 4√(x+7)`

So,
`(f\circ g)(x)=f[g(x)]= 4√(g(x)+1)` (Replacing
`x` as
`g(x)` in the given
`f(x)` expression)

Given that,
`h(x)=(f\circ g)(x)` . So, we will get.........

`4√(x+7)= 4√(g(x)+1)\\ \\ √(x+7)= √(g(x)+1)\\ \\ x+7=g(x)+1\\ \\ g(x)=x+7-1 = x+6`

Thus, the answer will be:
`g(x)= x+6`