Question

Given the functions f(x) = left parenthesis 2 x right parenthesis squared plus  x  minus 1 

Answer 1

I'm going to rewrite f(x) and g(x) so that I don't get confused. 

Based on your description: 

f(x) = (2x)$^{2}$ + x - 1 simplified to 4x$^{2}$ + x - 1

g(x) = x$^{2}$ + 3x - 3

Now we handle parts A-D.

A. f(x) + g(x)

We combine like terms. 

4x$^{2}$ + 5x$^{2}$ + x + 3x - 1 - 3 = 5x$^{2}$ + 4x - 4

B. f(x) - g(x)

Again combine like terms like normal except this time subtracting. 

4x$^{2}$ - x$^{2}$ + x - 3x - 1 - (- 3) = 3x$^{2}$ - 2x + 2

C. 2f(x) + 2g(x)

Multiply, then again CLT

2f(x) = 8x$^{2}$ + 2x - 2
2g(x) = 2x$^{2}$ + 6x - 6

Combine like terms to get 10x$^{2}$ + 8x - 8

D. 2f(x) - 2g(x) 

Use the same 2f(x) and 2g(x) terms and this time just subtract.

You get 6x$^{2}$ - 4x + 4