Please help me I’m lost

Question

Questions Given f (x) = 2x^2 – x and g(x) = x + 1, answer following:

1. Find (g•f)(-1).

2. Find (f•g)(-1).

3. Find (g•f)(x).

4. Find (f•g)(x).

5. Is (f•g) (x) = (g•f)(x)? Yes or No?

Answer 1

Another way to (g•f) is g(f(x)) or (g of f)(x)

1. g(f(-1)). To solve this first calculate f(-1) and then plug that answer into g. f(-1) is 3. g(3) is 4 so g(f(-1)) is 4.
2. f(g(-1)). First find g(-1) and then plug that answer into f. g(-1) is 0. f(0) is 0
3. g(f(x)). They already give you f(x) = 2x^2 - x. Plug this equation into g which then becomes g(2x^2 -x). Since g(x) = x + 1, we can replace x in this equation with 2x^2 -x. This becomes g(f(x)) = 2x^2 - x + 1
4. f(g(x)). g(x) = x+1. f(g(x)) then becomes f(x+1) which is 2(x+1)^2 - x + 1
5. We can see that they are not equal as the answers to part 4 and 5 are not equal. This shows that the order in which you concatenate functions matters as the answer is not the same both ways.

Answer 2

First 3 and 4. They demonstrate the form

f(g(x)) = 2(x + 1)² - (x + 1), the x in f(x) has been replace by g(x)

g(f(x)) = (2x² - x) + 1, the x in g(x) has been replaced by f(x)

To determine f(g(-1)) substitute -1 for x in the top equation.

To determine g(f(-1)) substitute -1 for x in the bottom equation

Can you do this and answer?