Evaluate the function for given values of the independent variable and simplify

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Pilot23

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I come across this math problem:
[MATH] f(x)=\frac{1}{\sqrt{x-1}} , when : \displaystyle\frac{f(x)-f(2)}{x-2} [/MATH]
I know this is the answer from the book :
[MATH]\displaystyle\frac{-1}{\sqrt{x-1}(1+\sqrt{x+1})} , x \neq 2 [/MATH]
but can someone help me in some way with this exercise, but step by step and well detailed? thank you.
 
Pilot23 said:
I come across this math problem:
[MATH] f(x)=\frac{1}{\sqrt{x-1}} , when : \displaystyle\frac{f(x)-f(2)}{x-2} [/MATH]
I know this is the answer from the book :
[MATH]\displaystyle\frac{-1}{\sqrt{x-1}(1+\sqrt{x+1})} , x \neq 2 [/MATH]
but can someone help me in some way with this exercise, but step by step and well detailed? thank you.
Click to expand...
You have NOT told us - EXACTLY what was the question!!
 
Yes I did here "but can someone help me in some way with this exercise, but step by step and well detailed? thank you."
 
No, you did not. You asked for help with an exercise but never stated what it was. You quoted one equation, one expression and an answer but failed to say what you wanted done.

Perhaps you wanted to know what 2f(x) equals or maybe f(x) = 11 or ......?

It is also against the forum policy for any helpers to give out step by step solutions. I myself am not going to get suspended from this site by giving you a solution to your problem. I take it that you failed to read the posting guidelines. Please read them.
 
The guidelines say to give the problem COMPLETELY AND EXACTLY.

You did not. You did not even tell us what topic you are studying so we might guess what the actual problem is. By any chance did you leave out “find f(x) … when x =“ Kind of an important clue as to what the problem is about.

The guidelines also say to show your work. You did not. If you cannot even start, at least tell us what stops you from even beginning.

I do not mind giving detailed steps, but I do mind doing your work for you on a poorly defined problem.
 
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Also, your title "evaluate the function for given values of the variable and simplify" is very misleading. You are askked to find the difference quotient for the function, f, between x and 2.

Are you able to find f(2)? It is, of course, \(\displaystyle f(2)= \frac{1}{\sqrt{2- 1}}= \frac{1}{\sqrt{1}}= 1\)
So \(\displaystyle f(x)- f(2)= \frac{1}{\sqrt{x-1}}- 1= \frac{1}{\sqrt{x- 1}}- \frac{\sqrt{x- 1}}{\sqrt{x- 1}}= \frac{1- \sqrt{x- 1}}{\sqrt{x- 1}}\).
 
HallsofIvy said:
Also, your title "evaluate the function for given values of the variable and simplify" is very misleading. You are askked to find the difference quotient for the function, f, between x and 2.

Are you able to find f(2)? It is, of course, \(\displaystyle f(2)= \frac{1}{\sqrt{2- 1}}= \frac{1}{\sqrt{1}}= 1\)
So \(\displaystyle f(x)- f(2)= \frac{1}{\sqrt{x-1}}- 1= \frac{1}{\sqrt{x- 1}}- \frac{\sqrt{x- 1}}{\sqrt{x- 1}}= \frac{1- \sqrt{x- 1}}{\sqrt{x- 1}}\).
Click to expand...
pilot23 has been banned for pofanity.
 
He posted it on MF, claimed he wasn't the same person and got ticked off at me for saying it, then apparently left.

(He was trying to ask how to prove that the difference quotient was that mess at the bottom. I tried to tell him it wasn't and he got mad, called me incompetent, and said he was going to leave.)

Oh, and he's 13.

-Dan
 
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