Question

Given f (x )equals 2 x minus 5 and g (x )equals 5 x squared​, first find f plus g​, f minus g​, ​fg, and StartFraction f Over g EndFraction . Then determine the domain for each function.

Answer 1

(f + g)(x) = 5x² + 2x - 5

Domain: All real numbers

(f - g)(x) = -5x² + 2x - 5

Domain: All real numbers

(fg)(x) = 10x³ - 25x²

Domain: All real numbers

(f/g)(x) =
`(2x-5)/(5x^2)`

Domain: (negative infinity, 0)U(0, positive infinity)

Explanation:

For f + g, we are simply adding the 2 together

Domain: All values of x work, as any value x outputs any value y

For f - g, we are simply subtracting the 2 together

Domain: All values of x work, as any value x outputs any value y

For f times g, we are simply multiplying (distributing) the 2 together

Domain: All values of x work, as any value x outputs any value y

For f divided by g, we are simply dividing (fraction) the 2 together

Domain: All values except for 0 work (undefined error), so asymptote at x = 0