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!

## Answer this Question

## Related Questions

- calculus - when working with composite functions, does fog=gof? how do i create ...
- advanced functions/precalculus - 1. The function f(x) = (2x + 3)^7 is the ...
- Math - Inverse Functions - Find the inverses of the following functions. y = 3(x...
- Algebra - Can anyone help me with this problem? I need to show all steps and ...
- Composite Functions - f(x)=(7x+28)/(x-3) and g(x)=(3x+28)/(x-7) Find: (fog)(x) (...
- CALCULUS - show that f(x) = x^2-1 (x is greater than and equal to 0) and g(x) = ...
- Calculus - Hi there, I need help with composition of functions. I need to find ...
- algebra functions - construct two composite functions, Evaluate each composite ...
- college algebra - find functions f anf g so that fog equals H H(x)=x^2+17 ...
- college algebra - given f(x)=4x-5, g(x)= x+5 over 4 Find (fog)(x). are these ...