Functions?

Question

I have been working on this problem for about an hour now and I still can't get it. Can someone helps me and show your work?

If f(x) = x^2 - x + 2 and h is not equal to 0, find:

1.) f(x + h) - f(x)
2.) f(x + h) - f(x) / h (all over h)

Answer 1

1)
(x+h)^2-x^2 (substitute in function values)
x^2+2xh+h^2-x^2 (Remove parentheses)
2xh+h^2 (cancel like terms)
2)
Substituting our work from step 1):
(2xh+h^2)/h
2x+h (exactly 1 "h" cancels from each term in the numerator, and the denominator becomes 1)

Answer 2

To find f(x+h), substitute (x+h) in place of x:

(x+h)^2 - (x+h) + 2

then, simplify that, and subtract f(x) from that result

For #2, just hit the answer to #1 with (1/h), which is the same as dividing each term by h.

Answer 3

f(x+h) = (x+h)^2 - (x+h) + 2 which simplifies to
x^2+2xh + h^2 - x - h + 2

f(x+h) - f(x) = (x^2 + 2xh + h^2 - x - h + 2) - (x^2 - x + 2) which
simplifes to
2xh + h^2 - h

factor out h: h(2x + h - 1)
if you put that over h, the h's cancel and that leave 2x + h - 1

Answer 4

To calculate f(x+h), simply substitute (x+h) for every occurance of (x) in the formula.

So, f(x+h) = (x+h)^2 -(x+h) +2
and f(x+h) - f(x) = (x+h)^2 - (x+h) +2 - x^2 + x - 2

This should get you started. Let me know if you need more help.

Answer 5

hey u know how to plot graph
just plot f(x) and plot f(x+h) by shifting axis (-h,0) where h is ne variable and bang u got the answer for first problem and automatically 2nd

Answer 6

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

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

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

once you open the brackets,

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

we can cancel out + and - x^2, x, and 2. remaining terms are...

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

we can factor out h since it is common in all terms...

f(x+h)-f(x)=h(2x+h-1)

divide by h
(f(x+h)-f(x))/h = (h(2x+h-1))/h

h is in numerator and denominator, cancels out each other...

(f(x+h)-f(x))/h = 2x+h-1

I guess you are looking for derivative by using definition of it...

Answer 7

f(x+h) - f(x) = (x+h)² - (x+h) + 2 - [x² - x +2]
= x² + 2hx + h² - x - h + 2 - x² + x - 2
= h² + 2hx - h

all that over h

= h + 2x -1