If f(x) = 2x^2 + 1 and g(x) = x^2 - 7, find (f - g)(x).

Step-by-step explanation:

If f(x)=3x^2-2x+4, then

f(x + h)

= 3(x + h)^2 -2(x + h) + 4

=3(x^2 + 2hx + h^2) - 2(x + h) +4

= 3x^2 + 6hx + 3h^2 - 2x -2h + 4

So

f(x+h)-f(x)

= 3x^2 + 6hx + 3h^2 - 2x -2h + 4 - (3x^2 - 2x + 4)

= 3x^2 + 6hx + 3h^2 - 2x -2h + 4 - 3x^2 + 2x - 4

= 6hx + 3h^2 - 2h

hello from mrbilldoesmath!

answer:

a(n) - a(n-1) -3

discussion:

this ones a bit interesting. given a(n) = 5 - 3n consider this:

a(n-1) = 5 - 3(n-1)

          = (5 - 3n) + 3             => but a(n) = 5 - 3n, the first term

          = a(n)   + 3                 => subtract 3 from both sides

a(n-1) -3 = a(n)  

or

a(n) - a(n-1) -3

you,

mrb

the first one, all those points on the line just make a strait line.