SOLUTION: How to solve whether or not the functions are inverses of each other? 1)F(x)=6x-7, g(x)=(x-6)/7 and 2) f(x)=3/(x+7), g(x)=(7x+3)/x

Algebra ->  Inverses -> SOLUTION: How to solve whether or not the functions are inverses of each other? 1)F(x)=6x-7, g(x)=(x-6)/7 and 2) f(x)=3/(x+7), g(x)=(7x+3)/x      Log On


   

Question 681109: How to solve whether or not the functions are inverses of each other?
1)F(x)=6x-7, g(x)=(x-6)/7
and
2) f(x)=3/(x+7), g(x)=(7x+3)/x
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Tell whether or not the functions are inverses of each other?
1)F(x)=6x-7, g(x)=(x-6)/7
and
2) f(x)=3/(x+7), g(x)=(7x+3)/x

If they are inverses, then their composite functions have to equal x

That is f(g(x))=x and g(f(x))=x.
1. f%28g%28x%29%29=f%28%28x-6%29%2F7%29
You will substitute g(x) in for the x's in f(x).
f%28g%28x%29%29=6%28%28x-6%29%2F7%29-7
f%28g%28x%29%29=%286x-36%29%2F7-7
Get a common denominator...
f%28g%28x%29%29=%286x-36%29%2F7-49%2F7
f%28g%28x%29%29=%286x-85%29%2F7
since it did not simplify to x, they are not inverses of each other.

2. f(g(x))=f((7x+3)/x)

f%28g%28x%29%29=3%2F%28%287x%2B3%29%2Fx%2B7%29
Multiply the top and the bottom by x to clear the complex fraction.
f%28g%28x%29%29=3x%2F%28x%287x%2B3%29%2Fx%2B7x%29
f%28g%28x%29%29=3x%2F%287x%2B3%2B7x%29
f%28g%28x%29%29=3x%2F%2814x%2B3%29
This also doesn't simplify to x and therefore are not inverses.
******************************************************************
Just to clarify....this is an example where they ARE inverses.
3. f%28x%29=3%2F%28x-1%29 and g%28x%29=%283%2Bx%29%2Fx
f%28g%28x%29%29=f%28%283%2Bx%29%2Fx%29
f%28g%28x%29%29=3%2F%28%28%283%2Bx%29%2Fx%29-1%29
to clear the complex fraction, multiply the top and bottom by x
f%28g%28x%29%29=3x%2F%28x%283%2Bx%29%2Fx-x%29
f%28g%28x%29%29=3x%2F%283%2Bx-x%29
f%28g%28x%29%29=3x%2F3
f%28g%28x%29%29=x
f(x) and g(x) ARE inverses in this case because f(g(x))=x.
*Note...g(f(x))=x as well....give it a try.
Hope that helped. Happy Calculating!!!!