Use function composition to show that f(x) and g(x) are inverses of each other. f(x)=2x-6; g(x)=(x+6)/2 - Show that f(g(x)) = x and that g(f(x)) = x

Question

lochana · Answer

$$f(x) = 2x - 6$$$$f(x) + 6 = 2x $$$$x = \frac{f(x) + 6}{2}$$$$hence\  g(x)\ is \ the \ inverse \ of \ f(x)$$

anonymous · Answer

Thank you so much lochana! I've been struggling with this problem forever!

lochana · Answer

so
$$g(x) = \frac{x+6}{2}$$

lochana · Answer

$$f(x) = 2x -6 $$$$f(g(x)) = 2g(x) -6 $$$$f(g(x)) = 2\frac{x+6}{2} -6 $$$$f(g(x)) = x+6 -6 $$$$f(g(x)) = x $$

lochana · Answer

$$g(x) = \frac{x + 6}{2}$$$$g(f(x)) = \frac{f(x) + 6}{2}$$$$g(f(x)) = \frac{2x -6 + 6}{2}$$$$g(f(x)) = x$$

anonymous · Answer

Thanks so much!