Question

Question 7 of 10

If h(x) = (fºg)(x) and h(x) = Vx+5, find g(x) if f(x) = (x+2.
Answer here

Answer 1

g(x) = x + 3

Explanation:

A composite function is a function that is written inside another function which means substituting one function into another function.

Ex: (fоg)(x) is a composite function, where x of f(x) is substituted by g(x)

∵ h(x) = (fоg)(x)

∵
`h(x)=√(x+5)`

∵
`f(x)=√(x+2)`

→ Substitute x of f(x) by g(x)

∴ (fоg)(x) =
`√(g(x)+2)`

→ Equate (fоg)(x) by h(x)

∴
`√(g(x)+2)=√(x+5)`

→ Cancel the roots from the two sides

∴ g(x) + 2 = x + 5

→ Subtract 2 from both sides

∴ g(x) + 2 - 2 = x + 5 - 2

∴ g(x) = x + 3