Question

For f(x)=(3x^2)+5and g(x)=7x-2,

a. Verify: g(x + 2) ≠ g(x) + g(2).


b. Find (f – g)(x).


c. Using the resulting function in (b), show that (f – g)(2) = f(2) – g(2).
(The work should be different for each side of the equation.)


d. Is (fg)(0) =(f/g)(0)? Explain.


e. Find (f(x+h)-f(x))/h , h ≠ 0.

Answer 1

The instructions appear quite clear, where does your problem arise?

I will do a)
Left Side = g(x+2) = 7(x+2) - 2
= 7x + 14 - 2 = 7x + 12

Right Side = g(x) + g(2)
= 7x - 2 + 12 - 2
= 7x +8

Thus g(x+2) ≠ g(x) + g(2)

do the others in a similar way