Which expression represents the composition [g o f](x) for the functions below? f(x) = 3x – 2 g(x) = 1 + 2x 6x – 1 6x + 3 6x + 1 6x – 3

For this case we have the following functions:

We must find

By definition of composition of functions we have to:

So:

We apply distributive property to the terms of parentheses:

We add common terms:

ANSWER

EXPLANATION

The given functions are:

and

We want to find the composite function,

We know that:

This implies that,

We substitute 3x-2 into g(x) to get;

We expand to get;

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4