Use the functions to evaluate the indicated expressions and simplify.

Question

I could use some help! Thanks in advance

f(x)=3x^2-2x g(x)=x^2+1

a. f(x+2)

Answer 1

The independent variable x acts as place holder.

So, if we are trying to evaluate f(x+2), we need to start with the function f(x) = 3x^2 - 2x.

Anywhere we see an x in f(x), we need to replace (making sure to use parentheses!) with (x+2).

f(x+2) = 3(x+2)^2 - 2(x+2) Distribute -2

= 3(x+2)(x+2) - 2x -4 FOIL (x+2)^2

= 3(x^2 + 2x + 2x + 4) - 2x - 4

= 3(x^2 + 4x + 4) - 2x - 4 Distribute 3

= 3x^2 + 12x + 12 - 2x - 4 Gather like terms and simplify

= 3x^2 + 10x + 8