Question

If h(x)=(fog)(x) and h(x) = sqrt x+5, find g(x) if f(x) = sqrtx+2

Answer 1

Answer: The value of g(x) is x+3.

Explanation:

Since we have given that

`h(x)=f\circ g(x)`

Here,

`h(x)=√(x+5)\\\\and\\\\f(x)=√(x+2)`

We need to find the value of g(x):

`f(x)=√(x+2)\\\\f(g(x))=√(g(x)+2)\\\\h(x)=√(g(x)+2)\\\\√(x+5)=√(g(x)+2)\\\\x+5=g(x)+2\\\\g(x)=x+5-2=x+3`

Hence, the value of g(x) is x+3.