SOLUTION: Hello, I am having trouble with this question. Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other. f(x)=3x-7 g(x)=x+3/7

Algebra ->  Inequalities -> SOLUTION: Hello, I am having trouble with this question. Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other. f(x)=3x-7 g(x)=x+3/7       Log On


   

Question 832815: Hello,
I am having trouble with this question.
Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other.
f(x)=3x-7
g(x)=x+3/7
I am absolutely lost on how to solve this question. Detailed explanation would be deeply appreciated. Thanks
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Not sure how you mean your g(x). As written you have x+3/7, as rendered, x%2B3%2F7.

f%28g%28x%29%29=3%28g%28x%29%29%2B7=3%28x%2B3%2F7%29-7
3x%2B9%2F7-7
%283x%2A7%29%2F7%2B9%2F7-7%2A7
%2821x%2B9-7%29%2F7
%2821x%2B2%29%2F7
-
Will that composition give x as the result?
NO.

You likely misunderstood what you read of g(x).
This definition is different: g%28x%29=%28x%2B3%29%2F7. Is this what you are really given?
f%28g%28x%29%29=3%28%28x%2B3%29%2F7%29-7
3%28x%2B3%29%2F7-7%2A7%2F7
%283x%2B9%29%2F7-49%2F7
%283x%2B9-49%29%2F7
%283x-40%29%2F7
Neither is this one x.
NOT the inverse of f(x).

The basic idea is if f(g(x))=x and g(f(x))=x, then f and g are inverses.

If you WANT to know the inverse of f(x), then try:
f%28g%28x%29%29=highlight_green%28x=3%28g%28x%29%29-7%29 and solve this for g(x).
x%2B7=3%2Ag%28x%29%29
%28x%2B7%29%2F3=%281%2F3%29%283%29g%28x%29
%28x%2B7%29%2F3=g%28x%29----------This is likely to be the inverse of f(x).