Question

Determine whether these two functions are inverses. Show your work please. f(x)=3x+27; g(x)= 1/3x+9

Answer 1

Answer:

Proved.

Step-by-step explanation:

The functions are:

1.) f(x) = 3x - 27 (* I am giving an answer using this equation. Perhaps you did't copy the question well!)

2.) g(x) = $\frac{1}{3} x$ + 9

If two functions are inverses of each other, then:

f(g(x)) = x and g(f(x)) = x situation must be satisfied.

f(g(x)) = 3($\frac{1}{3}x + 9$) + 27

We simply it to get;

f(g(x)) = x - 27 + 27 = x (*This is correct)

g(f(x)) = $\frac{1}{3}$(3x - 27) + 9 = x - 9 + 9 = x (* This is also correct!)