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.

Step-by-step explanation:

Since we have given that

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

Here,

$h(x)=\sqrt{x+5}\\\\and\\\\f(x)=\sqrt{x+2}$

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

$f(x)=\sqrt{x+2}\\\\f(g(x))=\sqrt{g(x)+2}\\\\h(x)=\sqrt{g(x)+2}\\\\\sqrt{x+5}=\sqrt{g(x)+2}\\\\x+5=g(x)+2\\\\g(x)=x+5-2=x+3$

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