Question

If f(x)= 3/x-4 and g(x)=2x, there is at least one value of x for which the composite function f(g(x)) cannot be evaluated.

What is that value of x? For what value(s) of x is it impossible to evaluate g(f(x))?

How do you figure this out?

Answer 1

As a first step, graph f(x) and find the discontinuity for the function f(x).
Call this point x0.

If this point x0 is found, x0=g(x) is not admissible in the composition f(g(x)), because x0 is not in the domain of f(x).

Since x0=g(x)=2x, we conclude that x=x0/2 is not an admissible value of x in f(g(x)) because
f(g(x0/2)) = f(2(x0/2))=f(x0) which is undefined.

You can find the value of x in the second part using a similar argument.

If you need further help, please post.