Question

Help!!
I learned this in Business Cal, not learning this in Pre Cal.. I cannot figure how to get to the right answer...

Given: f(x)=3x-(1/x) -3
Simplify: f(x+h)-f(x)/h

The answer is: 13+6h/4+2h

I cannot figure out how to get that answer. HELP PLEASE
!

Answer 1

So write out f(x) but then instead of writing just plain x, write it in parenthesis as (x).

Then it will be obvious when you write f(x+h), since everywhere you see an (x) you just write (x+h).

Answer 2

i FORGOT TO ADD THAT X=2

Answer 3

If phi isn't typing up a long explanation, I'll happily walk you through whatever you need help with if you show your steps and correct you if you make any mistakes.

Answer 4

Ok. I get replacing x with the equation f(x) ... I started out with putting x=2 into f(x) and got 2.5. Then I placed it in to the formula like this ...

f(2.5+h)-f(2.5)/h

and now i am lost ...

Answer 5

you start with
\[ f(x)= 3x - \frac{1}{x} - 3\]
to find f(x+h) replace "x" with "x+h" in the definition
\[ f(x+h)= 3(x+h) - \frac{1}{(x+h)} - 3 \\ f(x+h)= 3x+3h - \frac{1}{(x+h)} - 3\]

now find f(x+h) - f(x):
\[ f(x+h)-f(x)= 3x+3h - \frac{1}{(x+h)} - 3 - (3x - \frac{1}{x} - 3)\]

distribute the -1 over the parens:
\[ = 3x+3h - \frac{1}{(x+h)} - 3 -3x + \frac{1}{x} +3 \\ = 3h +\left(\frac{1}{x} - \frac{1}{(x+h)} \right)\]

Answer 6

that mess simplifies to
\[3 h + \frac{h}{x(x+h) } \]
divide by h to get (f(x+h) - f(x)) / h

\[ 3 + \frac{1}{x(x+h)} \]

Answer 7

OMG THAT MAKES SENSE!! Then I plug in x=2 to get

Answer 8

I plugging in x first and thats where I was lost.

Answer 9

if x= 2 , you get
\[ 3 + \frac{1}{2(2+h) } \\ 3+ \frac{1}{4+2h} \]
if we put that over a common denominator, I think we get your result

Answer 10

to get = 3+(1/2(2+h) ..... (1/4+2h)+(3/1) ....

Answer 11

one sec typing .. i wanna see if i do this right :)

Answer 12

(1/4+2h)+(12+6h/4+2h) = 13+6h/4+2h

Answer 13

did i do all that math right? i want to make sure when i have another questions like this on a quiz/exam i am doing this all right :)

Answer 14

You could have done the problem using
(f(2+h) - f(2))/h
(not 2.5!)

Answer 15

yes that matches your answer up top

Answer 16

oh .. i understand the first explanation first.. i am good to go! thank you for your help! :)