Can anyone find this answer?

Question

if g(x) = 2-x^2, find g(3+h) - g(3)

-----------------

h

only the g(3+h) - g(3) is divided by h

Answer 1

[g(3+h) - g(3)]/h=

[2-(3+h)^2-2+9]/h=

(2-9-h^2-6h+7)/h=

(-h^2-6h)/h=

-h-6

Answer 2

((2 - (3 + h)^2) - (2 - 3^2))/h

= ((2 - (9 + 6h + h^2)) - (2 - 3^2))/h

= (2 - 9 - 6h - h^2) - (2 - 9))/h

= (2 - 9 - 6h - h^2 - 2 + 9))/h

= (-6h - h^2)/h

= (h(-6 - h))/h

= -6 - h = Final Answer

Answer 3

You function is:

g(x) = 2 - x²

To find g(3 + h) - g(3), plug in what you have and simplify:

g(3 + h) = 2 - (3 + h)²

g(3 + h) = 2 - (8 + 6h + h²)

g(3 + h) = 2 - 8 - 6h - h²

g(3 + h) = -h² - 6h - 6

Now to find g(3):

g(3) = 2 - (3)²

g(3) = 2 - 9

g(3) = -7

Now find the difference of the two:

g(3 + h) - g(3) = -h² - 6h - 6 - (-7)

g(3 + h) - g(3) = -h² - 6h - 6 + 7

g(3 + h) - g(3) = -h² - 6h + 1