For f(x)= x+5 and g(x)=4x+2
find (fog)(x) and (gof)(x)

Composing functions means that the input of the outer functions is the output of the inner function.

In fact, you can rewrite the circle notation as

So, we can substitute g(x) with its expression:

And since f(x)=x+5, we simply have to add 5 to its input:

Similarly, we have, substituting f with its expression,

And since g(x)=4x+2, we have to multiply the input by 4 and add 2:

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction