SOLUTION: Find f(g(x)) and g(f(x)) and determine whether the functions f and g are inverses of each other. f(x)=5x-6 g(x)=(x+5)/6

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Question 312514: Find f(g(x)) and g(f(x)) and determine whether the functions f and g are inverses of each other.
f(x)=5x-6
g(x)=(x+5)/6
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28g%29=5%28%28x%2B5%29%2F6%29-6=%281%2F6%29%285x%2B25-36%29=%281%2F6%29%285x-11%29 which does not equal x
g%28f%29=%281%2F6%29%285x-6%2B5%29=%281%2F6%29%285x-1%29 which also does not equal x
No, they are not inverse functions.
.
.
.
Find the inverse by interchanging x and y in the original f(x) and solving for y.
f%28x%29=y=5x-6
x=5y-6
x%2B6=5y
highlight%28g%28x%29=y=%281%2F5%29%28x%2B6%29%29
Now,
f%28g%29=5%28%281%2F5%29%28x%2B6%29%29-6=x%2B6-6=x