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)= 1/5x-7/5 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+7/5-7/5=x

You do the other.

- Algebra -
**MathMate**, Wednesday, July 29, 2009 at 9:03am
f(x)=5x+7

g(x)=(1/5)x-7/5=(x-7)/5

(f⁰g)(x)

= f(g(x))

= f((x-7)/5)

= 5((x-7)/5)+7

= x-7 + 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)= 1/5x-7/5

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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