SOLUTION: Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x)=8/x and g(x)=8/x show work

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Question 644387: Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
f(x)=8/x and g(x)=8/x
show work
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
f(x)=8/x

f(g(x))=8/(g(x))

f(g(x))=8/(8/x)

f(g(x))=(8/1)/(8/x)

f(g(x))=(8/1)*(x/8)

f(g(x))=(8x)/(1*8)

f(g(x))=(8x)/(8)

f(g(x))=x

The same works in reverse

g(x)=8/x

g(f(x))=8/(f(x))

g(f(x))=8/(8/x)

g(f(x))=(8/1)/(8/x)

g(f(x))=(8/1)*(x/8)

g(f(x))=(8x)/(1*8)

g(f(x))=(8x)/(8)

g(f(x))=x

So these both in conjunction show that f and g are inverses of each other.

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