Posted by Alicia on Wednesday, July 29, 2009 at 3:30am.
Use composition of functions to show that the functions f(x) = 5x + 7 and
g(x)= 1/5x7/5 are inverse functions. That is, carefully show that (fog)(x)= x and (gof)(x)= x.

Algebra  bobpursley, Wednesday, July 29, 2009 at 9:01am
g(f(x))=1/5 (5x+7) 7/5
= x+7/57/5=x
You do the other.

Algebra  MathMate, Wednesday, July 29, 2009 at 9:03am
f(x)=5x+7
g(x)=(1/5)x7/5=(x7)/5
(f⁰g)(x)
= f(g(x))
= f((x7)/5)
= 5((x7)/5)+7
= x7 + 7
= x
(g⁰f)(x)
= g(f(x))
= g(5x+7)
= ((5x+7)7)/5
= 5x/5
= x
I do not know how your book displays the expression, but the first term of
g(x)= 1/5x7/5
offers two possible interpretations, namely (1/5)x or 1/(5x). You might even have been able to solve the problem if it wasn't for the ambiguity.

Algebra  Alicia, Wednesday, July 29, 2009 at 1:32pm
Thank you! I got a ton more of these to do, so you helped greatly! Thanks!
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