Let f(x)=2x^2+x-3 and g(x)=x-1. Perform the indicated operation, then find the domain.
(f*g)(x)
Answers:
A. 2x^3-x^2-4x+3; domain: all real numbers
B. 2x^3+x^2-3x; domain: all real numbers
C. 2x^3+x^2+4x-3; domain: negative real numbers
D. 2x^2+x-3x+3; domain: positive real numbers
I'd appreciate any help I can get! I don't want just the answer, I'd like to know the steps too so I can figure out how to do this in the future!
Multiplying the two functions together using the Distributive Property, we get (2x²+x-3)*(x-1)=2x³+x²-3x-2x²-x+3= 2x³-x²-4x+3. In addition, since any value x can be plugged into 2x³-x²-4x+3, A is your answer!
