SOLUTION: use the composition of functions to show that f^-1 is as given f(x)=1/2x-3, f^-1(x)=2(x+3) please show your work

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: use the composition of functions to show that f^-1 is as given f(x)=1/2x-3, f^-1(x)=2(x+3) please show your work      Log On


   

Question 1139298: use the composition of functions to show that f^-1 is as given f(x)=1/2x-3, f^-1(x)=2(x+3) please show your work
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
To prove f%28x%29 and f%5E-1%28x%29 we need to show
(f∘f%5E-1)(x)=x and (f%5E-1∘f)(x)=x


f%28x%29 ∘f%5E-1%28x%29=f%28f%5E-1%28x%29%29
f%28x%29 ∘ f%5E-1%28x%29=f%282%28x%2B3%29%29
f%28x%29 ∘ f%5E-1%28x%29=%281%2F2%29%282%28x%2B3%29%29+-3
f%28x%29 ∘ f%5E-1%28x%29=x%2B3+-3
f%28x%29 ∘ f%5E-1%28x%29=x =>proven


f%5E-1%28x%29 ∘ f%28x%29=f%5E-1%28f%28x%29%29
f%5E-1%28x%29 ∘ f%28x%29=f%5E-1%28%281%2F2%29x-3%29%29
f%5E-1%28x%29 ∘ f%28x%29=2%28%281%2F2%29x-3%2B3%29%29
f%5E-1%28x%29 ∘ f%28x%29=x-3%2F2%2B3%2F2
f%5E-1%28x%29 ∘ f%28x%29=x=>proven