Question

If f(x) = 2x and g(x) = 9x, which of the following statements is true?

Answer 1

Composing functions means to use the output of the inner function as the input for the outer one. It gets really clear and simple if you explicitly write it out:

$(f\circ g)(x)=f(g(x))$

Now substitute $g(x)=9x$:

$(f\circ g)(x)=f(g(x))=f(9x)$

Now, since $f(x)=2x$, we know that $f(x)$ gives as output twice the input. In this case, the input is $g(x)=9x$, so the output will be twice as much:

$(f\circ g)(x)=f(g(x))=f(9x)=18x$

Note that we also have

$(g\circ f)(x)=g(f(x))=g(2x)=9\cdot 2x=18x$