Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

Thanks so much!