SOLUTION: Use composition of functions to show that the functions f(x) = 5x – 2 and g(x) = (x+2)/5 are inverse functions. That is, show that (f of g)(x)=x and show that (g of f)(x) =x I

Algebra ->  Functions -> SOLUTION: Use composition of functions to show that the functions f(x) = 5x – 2 and g(x) = (x+2)/5 are inverse functions. That is, show that (f of g)(x)=x and show that (g of f)(x) =x I       Log On


   

Question 192113: Use composition of functions to show that the functions f(x) = 5x – 2 and g(x) = (x+2)/5 are inverse functions. That is, show that (f of g)(x)=x and show that (g of f)(x) =x
I am not sure how to approach this assignment!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: (f o g)(x) means f(g(x)) and (g o f)(x) means g(f(x))


f%28x%29=5x-2 Start with the first function


f%28g%28x%29%29=5%28%28x%2B2%29%2F5%29-2 Plug in g%28x%29=%28x%2B2%29%2F5


f%28g%28x%29%29=cross%285%29%28%28x%2B2%29%2Fcross%285%29%29-2 Cancel out like terms


f%28g%28x%29%29=x%2B2-2 Simplify


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


--------------------------------------------------

g%28x%29=%28x%2B2%29%2F5 Start with the second function


g%28f%28x%29%29=%28%285x-2%29%2B2%29%2F5 Plug in f%28x%29=5x-2


g%28f%28x%29%29=%285x%29%2F5 Combine like terms.


g%28f%28x%29%29=%28cross%285%29x%29%2Fcross%285%29 Cancel out like terms.


g%28f%28x%29%29=x Simplify



Since we've shown that f%28g%28x%29%29=x and g%28f%28x%29%29=x, this means that the two functions are inverses of each other.