Question

g(f(x)) and
f(f(x))
when f(x)=3x/x-1
g(x)=x/x-3

Answer 1

@Directrix

Answer 2

@Mertsj

Answer 3

\[g(f(x))=\frac{\frac{3x}{x-1}}{\frac{3x}{x-1}-3}=\frac{3x}{3x-3(x-1)}=\frac{3x}{3}=x\]

Answer 4

\[f(g(x))=\frac{3\times \frac{x}{x-3}}{\frac{x}{x-3}-1}=\frac{3x}{x-(x-3)}=\frac{3x}{3}=x\]

Answer 5

So we see that the functions f and g are inverse functions because by definition if f(g(x))=x and g(f(x))=x, then f and g are inverse functions.

Answer 6

right :) so how about f(f(x))

Answer 7

Can you try that now?

Answer 8

3*3x/x-1/3x/x-1

Answer 9

@Mertsj

Answer 10

??

Answer 11

You forgot the -1 in the denominator