Question

If h(x)=(f o g) (x) and h(x)=√x+5, find g(x) if f(x)=√x+2

Answer 1

h(x)=(f o g)(x)=f(g(x)) =>

`√(x)+5=√(g(x))+2`

`√(g(x))=√(x)+5-2`

`√(g(x))=√(x)+3`

`g(x)=(√(x)+3)^2`

`=(x+6√(x)+9)^2`

Answer 2

we are given

`h(x)=(fog)(x)`

we can write it as

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

`f(x)=√(x+2)`

now, we can replace x as g(x)

`f(g(x))=√(g(x)+2)`

`h(x)=√(g(x)+2)`

`h(x)=√(x+5)`

now, we can equate them

`√(x+5)=√(g(x)+2)`

now, we can solve for g(x)

Take square both sides

`(√(x+5))^2=(√(g(x)+2))^2`

`x+5=g(x)+2`

now, we can solve for g(x)

Subtract both sides by 2

`x+5-2=g(x)+2-2`

`x+3=g(x)`

`g(x)=x+3`.............Answer