# How do you find (g o f)(x) given #f(x)= x/(x-2)#, #g(x)=3/x#?

To find ( (g \circ f)(x) ), first find ( f(x) ) and then substitute it into ( g(x) ).

Given ( f(x) = \frac{x}{x - 2} ) and ( g(x) = \frac{3}{x} ):

- Substitute ( f(x) ) into ( g(x) ):

[ g(f(x)) = g\left(\frac{x}{x - 2}\right) ]

- Substitute ( \frac{x}{x - 2} ) for ( x ) in ( g(x) ):

[ g(f(x)) = g\left(\frac{x}{x - 2}\right) = \frac{3}{\frac{x}{x - 2}} ]

- Simplify:

[ g(f(x)) = \frac{3(x - 2)}{x} ]

So, ( (g \circ f)(x) = \frac{3(x - 2)}{x} ).

By signing up, you agree to our Terms of Service and Privacy Policy

Simplify.

By signing up, you agree to our Terms of Service and Privacy Policy

- Is the function #f(x) = x^6-2x^2+3# even, odd or neither?
- How do you find the end behavior of #f(x) = -x^2(1-2x)(x+2)#?
- How do you find vertical, horizontal and oblique asymptotes for #x/(1-x)^2#?
- How do you find vertical, horizontal and oblique asymptotes for #(x^2-x-8)/ (x+1)#?
- How do you find the inverse of #f(x)=9 x-4# and is it a function?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7