Question

what is $(hcdot k)(x)$ if $h(x)=2x^{2}+3x-1$ and $k(x)=x-1$?

Explanation:

Step1: Define function multiplication

$(h \cdot k)(x) = h(x) \cdot k(x)$

Step2: Substitute given functions

$(h \cdot k)(x) = (2x^2 + 3x - 1)(x - 1)$

Step3: Distribute each term

$= 2x^2(x-1) + 3x(x-1) -1(x-1)$

Step4: Expand individual products

$= 2x^3 - 2x^2 + 3x^2 - 3x - x + 1$

Step5: Combine like terms

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

Answer:

$2x^3 + x^2 - 4x + 1$