1.) If f(x)=x^2 and g(x)=4x-5, then fg(x)=4x^3-5x^2? True or False?

Question

My answer: True

2.) If f(x) =1/x and g(x)=1/x^2, find (g/f)(x).

My answer: I need help with this one.

Answer 1

(fg)(x) = f(x)*g(x) = (x^2)(4x-5) = 4x^3 - 5x^2

(g/f)(x) = g(x)/f(x)
= (1/x^2) / (1/x) = 1/x^2 * x/1 = x/x^2 = 1/x