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solmaris [256]
3 years ago
7

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

Mathematics
1 answer:
Alla [95]3 years ago
4 0

Answer:

Proved.

Step-by-step explanation:

The functions are:

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

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 (*<em>This is correct)</em>

<em />

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

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