1. Given f(x)=2x+3 and g(x)=x-4,
Find:
a. (f+g)(x)
b. (f-g)(x)
c. (f.g)(x
Answer (1)
Answer:Here's how to find the requested operations on the functions f(x) and g(x): a. (f + g)(x) - Definition: (f + g)(x) means you add the two functions together.- Calculation:(f + g)(x) = f(x) + g(x)(f + g)(x) = (2x + 3) + (x - 4)(f + g)(x) = 3x - 1 b. (f - g)(x) - Definition: (f - g)(x) means you subtract g(x) from f(x).- Calculation:(f - g)(x) = f(x) - g(x)(f - g)(x) = (2x + 3) - (x - 4)(f - g)(x) = x + 7 c. (f · g)(x) - Definition: (f · g)(x) means you multiply the two functions together.- Calculation:(f · g)(x) = f(x) · g(x)(f · g)(x) = (2x + 3) · (x - 4)(f · g)(x) = 2x² - 5x - 12 Summary: - (f + g)(x) = 3x - 1- (f - g)(x) = x + 7- (f · g)(x) = 2x² - 5x - 12
