SOLUTION: show that ((( f(x)=3x-4 and g(x)=(x+4)/3 ))) are inverses

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Question 153022: show that ((( f(x)=3x-4 and g(x)=(x+4)/3 ))) are inverses
Found 2 solutions by vleith, jim_thompson5910:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
When functions are invereses of each other, if you take (f(g(x)), you get x back.
Basically, the second function 'undoes' what the first one does.
f%28x%29+=+3x-4
f%28g%28x%29%29+=+3+%28%28x%2B4%29%2F3%29+-+4
f%28g%28x%29%29+=+%28x%2B4%29+-+4
f%28g%28x%29%29+=+x+

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=3x-4 Start with the first function.


f%28g%28x%29%29=3%28%28x%2B4%29%2F3%29-4 Plug in g%28x%29=%28x%2B4%29%2F3.


f%28g%28x%29%29=x%2B4-4 Multiply


f%28g%28x%29%29=x Combine like terms


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g%28x%29=%28x%2B4%29%2F3 Start with the second function.


g%28f%28x%29%29=%283x-4%2B4%29%2F3 Plug in f%28x%29=3x-4


g%28f%28x%29%29=%283x%29%2F3 Combine like terms.


g%28f%28x%29%29=x Reduce.


Since f%28g%28x%29%29=x and g%28f%28x%29%29=x, this shows that the two functions are inverses of one another.