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

• g(x) = x + 3

Explanation:

Given

• h(x) = (f ο g)(x)
• h(x) =
  `√(x+5)`
• f(x) =
  `√(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):

• 
  `√(x+5)` =
  `√(g(x)+2)`
• x + 5 = g(x) + 2
• x + 3 = g(x)
• g(x) = x + 3