Question

If f(x) = 3x - 2 and g(x) = 2x + 1, find (f-g)(x)

A. 5x - 1
B. 3 - x
C. x - 3
D. 5x - 3

Answer 1

Hey there.

When subtracting monomials, it's imperative that you subtract the proper terms. You cannot subtract or add a number from a variable, and you cannot do the same the other way around (unless you are multiplying).

Here's an example;
(2x + 1) + (3x + 3);
Add our variables.
2x + 3x = 5x
Add our numbers.
1 + 3 = 4.
Our final expression is 5x + 4.

Let's apply this knowledge to our current function.

f = 3x - 2
g = 2x + 1

f - g;
(3x - 2) - (2x + 1)
Remember to flip all signs of the variables and numbers to the right of the subtraction sign.
(3x - 2) - 2x - 1;
3x - 2x = x
-2 -1 = -3

We are left with x - 3.

Your answer is C.)

I hope this helps!

Answer 2

(f - g)(x) means f(x) - g(x)

So, you just input the function of f(x) and g(x) altogether, then simplify it.
(f - g)(x)
= f(x) - g(x)
= 3x - 2 - (2x + 1)
= 3x - 2 - 2x - 1
= x - 3

The answer is c