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

Answer:

g(x) = x + 3

Step-by-step 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)

∵ $h(x)=\sqrt{x+5}$

∵ $f(x)=\sqrt{x+2}$

→ Substitute x of f(x) by g(x)

∴  (fоg)(x) = $\sqrt{g(x)+2}$

→ Equate (fоg)(x) by h(x)

∴ $\sqrt{g(x)+2}=\sqrt{x+5}$

→ 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