Question

If p(x)=2x^2-4x and q(x)= x-3 what is (p•q)(x)

Answer 1

The use of the symbol • in (p•q)(x) is confusing.

You may be using it to indicate multiplication or to indicate composition of functions.

The operation and the results will be different in each case.

So, make sure that you interpret the problem correctly. I will do the problem for the two cases to help you.

1) if • means multiplication:

use the distributive property:

(p•q)(x) = (2x^2 - 4x) (x - 3) = 2x^3 - 6x^2 - 4x^2 + 12 x = 2x^3 - 10x^2 + 12x

2) if • means compositon of functions:

=> (p•q)(x) = p [ q(x)] = p [ x -3] = 2 (x - 3)^2 - 4(x - 3)

= 2[x^2 - 6x + 9] - 4x + 12 = 2x^2 - 12x + 18 - 4x + 12 = 2x^2  - 16x + 30

Then, only make sure of the use of the symbol • in (p•q)(x) , which you can find in the context of the question.