Functions? I don't understand this question or how to do it?

Question

Here's the question:

f(x)=x^2-5

find (f(x+h)-f(x))/h

I don't understand how to do these complicated ones. The ones we did before were like f(x)=3x+5 find f(-2). Any help would be appreciated! Thanks in advance!

Answer 1

When you were given f(x) = 3x + 5 and asked to find f(-2), you proceeded to replace every occurrence of x with -2. The idea is the same when asked to find the value of the function anywhere else.

When f(x) = x^2 - 5, then f(x + h) = (x + h)^2 - 5 = x^2 + 2xh + h^2 - 5. Easy enough? Now (f(x + h) - f(x))/h =
[x^2 +2xh + h^2 - 5 - (x^2 - 5)]/h =
[2xh + h^2]/h = [2x + h].

Answer 2

f(x)=x^2-5

find (f(x+h)-f(x))/h


f(x +h ) = ?

just replace x by (x +h) in f(x) =x^2 -5

f(x+h) = (x +h)^2 -5
f(x) = x^2 -5

f(x +h) -f(h) = (x +h)^2 -5 - x^2 +5 =
(x +h)^2 -x^2 = (x +h -x)(x+h +x) = h(2x+h)

(f(x+h)-f(x))/h = (2x+h)

when h -->0 ; f '(x) ---> 2x

that is the definition of the derivative of f(x) = x^2 -5

Answer 3

f(x)=x^2 - 5
find (f(x + h) - f(x)) / h

f(x + h) = (x + h)^2 - 5
f(x + h) - f(x) = (x^2 + 2hx + h^2 - 5) - (x^2 - 5) = 2hx + h^2

(f(x + h) - f(x)) / h = h(2x + h) / h = 2x + h.

Answer 4

You just put the function in:

f(x) = x² - 5

Therefore:

(f(x + h) - f(x)) / h

= (x² - 5 + h - (x² - 5)) / h

Multiply out of brackets:

(x² - 5 + h - x² - 5) / h

= h / h

= 1

Answer 5

this time u still substitute what the function is. so if it was f(x+h), then u would substitute the x with x+h...its not absolute that u will get a variable that exuals a number