Question

Using composition of functions, determine if the two functions are inverses

of each other.
F(x)=√x-6
G(x) = (x+6)²
OA. Yes, but only within the domain x ≥ 0.
OB. No, because the composition does not result in an answer of x.
OC. Yes, because F(x) is equal to - G(x).
OD. No, because the functions contain different operations.

Answer 1

A. Yes, but only within the domain x ≥ 0

Step-by-s+tep explanation:

What you need to know to solve the question:

1. To find an inverse function (f⁻¹(x)) of f(x), rearrange the equation in terms of f(x), in other words, it should be in the form of x = ...

2. Rules of rearranging equations

3. The domain of √x is: x ≥ 0, since you cannot find the square root of a negative number (i.e. < 0)

Find the inverse function of F(x):

According to principles 1 and 2:

F(x) = √x - 6

F(x) + 6 = √x

(F(x) + 6)² = x

x = (F(x) + 6)²

So, the inverse function is:

F⁻¹(x) = (x + 6)²

And since:

G(x) = (x + 6)²

G(x) = F⁻¹(x)

Therefore, the answer is, also in light of principle 3:

A. Yes, but only within the domain x ≥ 0