Question

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

g(x) = x squared plus 3 x minus 3

Find:

A. f(x) + g(x)

B. f(x) - g(x)

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

D. 2f(x) -2g(x)

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