Question

State if the given functions are inverses.
1)
F(x)=1/2x -2
g(x) = 2x + 4

Answer 1

Yes

Explanation:

• if
  `f(x)=(1)/(2)x-2` then what is
  `f^-1(x)` (the inverse of f(x)? let's find out
• 
  `f(x)=(1)/(2)x-2\\y=(1)/(2)x-2` make f(x) into y
• Then make y into x and make x into y so
  `x=(1)/(2)y-2`
• 
  `x=(1)/(2)y-2` now get the new y on the left and everything else on the right
• 
  `x=(1)/(2)y-2\\x+2=(1)/(2)y\\2(x+2)=(2)(1)/(2)y\\y=2x+4` now make y = g(x)
• 
  `g(x)=2x+4`
• So you found the inverse of f(x) and it is the same as g(x), so the functions are inverses of each other