Question

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

Answer 1

Answer:

• g(x) = x + 3

Step-by-step explanation:

Given

• h(x) = (f ο g)(x)
• h(x) = $\sqrt{x+5}$
• f(x) = $\sqrt{x+2}$

To find

• g(x)

Solution

We know that:

• (f ο g)(x) = f(g(x))

Substitute x with g(x) and solve for g(x):

• $\sqrt{x+5}$ = $\sqrt{g(x)+2}$
• x + 5 = g(x) + 2
• x + 3 = g(x)
• g(x) = x + 3