SOLUTION: Consider the function. f(x)= 1/2x + 1 a. Find the inverse of f(x) and name it g(x). Show and explain your work. b. Use function composition to show that f(x) and g(x) are inverse

Algebra ->  Functions -> SOLUTION: Consider the function. f(x)= 1/2x + 1 a. Find the inverse of f(x) and name it g(x). Show and explain your work. b. Use function composition to show that f(x) and g(x) are inverse      Log On


   

Question 997925: Consider the function. f(x)= 1/2x + 1
a. Find the inverse of f(x) and name it g(x). Show and explain your work.
b. Use function composition to show that f(x) and g(x) are inverses of each other.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=+%281%2F2%29x+%2B+1
a. Find the inverse of f%28x%29 and name it g%28x%29. Show and explain your work.
note: f%28x%29+=y
y=+%281%2F2%29x+%2B+1.....to find inverse, swap x and y
x=+%281%2F2%29y+%2B+1....solve for y
x-1=+%281%2F2%29y+
y=%28x-1%29%2F%281%2F2%29
y=2%28x-1%29
y=2x-2-> inverse g%28x%29
so +g%28x%29=2x-2

b. Use function composition to show that f%28x%29 and g%28x%29 are inverses of each other.
if f%28x%29 and g%28x%29 are inverses of each other, than %28f+o+g%29%28x%29+ will end up with just "x", so we will have:
%28f+o+g%29%28x%29=x
let's check it:
%28f+o+g%29%28x%29=f%28g%28x%29%29
%28f+o+g%29%28x%29=f%282x-2%29
%28f+o+g%29%28x%29=%281%2F2%29%282x-2%29+%2B+1
%28f+o+g%29%28x%29=2x%2F2-2%2F2%2B+1
%28f+o+g%29%28x%29=x-1%2B+1
%28f+o+g%29%28x%29=x=> proof that f%28x%29 and g%28x%29 are inverses of each other