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)) =>
$\sqrt{x}+5=\sqrt{g(x)}+2$
$\sqrt{g(x)}=\sqrt{x}+5-2$
$\sqrt{g(x)}=\sqrt{x}+3$
$g(x)=(\sqrt{x}+3)^2$
$=(x+6\sqrt{x}+9)^2$

Answer 2

we are given

$h(x)=(fog)(x)$

we can write it as

$h(x)=f(g(x))$

$f(x)=\sqrt{x+2}$

now, we can replace x as g(x)

$f(g(x))=\sqrt{g(x)+2}$

$h(x)=\sqrt{g(x)+2}$

$h(x)=\sqrt{x+5}$

now, we can equate them

$\sqrt{x+5}=\sqrt{g(x)+2}$

now, we can solve for g(x)

Take square both sides

$(\sqrt{x+5})^2=(\sqrt{g(x)+2})^2$

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

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