SOLUTION: Determine whether the functions f(x) = 6x and g(x) = x/6 are inverse functions.

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Question 1082185: Determine whether the functions f(x) = 6x and g(x) = x/6 are inverse functions.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's find f(g(x)).

f%28x%29+=+6x Start with the outer most function f(x)

f%28g%28x%29%29+=+6%28g%28x%29%29 Replace every copy of x with g(x)

f%28g%28x%29%29+=+6%28x%2F6%29 Replace the g(x) on the right side with x/6

f%28g%28x%29%29+=+x Simplify

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Now let's find g(f(x))

g%28x%29+=+x%2F6 Start with the outer most function g(x)

g%28f%28x%29%29+=+%28f%28x%29%29%2F6 Replace every copy of x with f(x)

g%28f%28x%29%29+=+%286x%29%2F6 Replace the f(x) on the right side with 6x

g%28f%28x%29%29+=+x Simplify

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Since f%28g%28x%29%29+=+x and g%28f%28x%29%29+=+x for all real numbers x, this means that f(x) and g(x) are inverses of each other.