1. ## Composite functions?

My first question is how would I multiply this

(x^2+2(delta)x+delta(x)^2) (x+delta(x))

My second questions is

Evaluate the function at the given values of the independent variable.

f(x)= 1/square root (x-1)

f(x)-f(2)/(x-2)

Can anyone show me how to do this one?

2. ## Re: Composite functions?

First question:
Is delta a constant or? ...

3. ## Re: Composite functions?

My first question is how would I multiply this

(x^2+2(delta)x+delta(x)^2) (x+delta(x))
$\displaystyle (x^2 + 2\delta(x) + {\delta}^2 (x))(x + \delta(x)) = x^3 + (2x + x^2)\delta(x) + (x+2){\delta}^2 (x) + {\delta}^3 (x)$

My second questions is

Evaluate the function at the given values of the independent variable.

f(x)= 1/square root (x-1)

f(x)-f(2)/(x-2)
$\displaystyle f(x) = \frac{1}{\sqrt{x-1}}$
$\displaystyle f(2) = 1$
$\displaystyle f(x) - \frac{f(2)}{x-2} = \frac{1}{\sqrt{x-1}} - \frac{1}{x-2}$

Kalyan.

4. ## Re: Composite functions?

@kalyanram:
Why do you calculate f(x-2)? I don't see that, just:
f(x)-f(2)/(x-2) not f(x)-f(2)/f(x-2).

Or do I miss something? ...

5. ## Re: Composite functions?

I am kind of confused when you get to the f(x-2)= 1/square root (x-3) part?

6. ## Re: Composite functions?

It would be far easier to start off by writing
$\displaystyle f(x)=\frac{1}{\sqrt{x-1}}$ as $\displaystyle f(x)=\frac{\sqrt{x-1}}{x-1}.$

7. ## Re: Composite functions?

Why do you calculate f(x-2)? I don't see that, just:
f(x)-f(2)/(x-2) not f(x)-f(2)/f(x-2).

Or do I miss something? ...
That was a mistake indeed corrected it.

8. ## Re: Composite functions?

Dang it I think I used incorrect notation when writting this

I meant

(f(x)-f(2))/(x-2)

9. ## Re: Composite functions?

f(2) is already calculated by kalyanram so you just have to fill in ...

10. ## Re: Composite functions?

Well this is what I did

I took Plato way of writing it

square root(x-1)/(x-1)-(1/1)

square root ((x-1)/(x-1)-(x-1)/(x-1))/((x-2)) I hope what I wrote makes sence

11. ## Re: Composite functions?

If $\displaystyle f(x)=\frac{\sqrt{x-1}}{x-1}$ then $\displaystyle f(2)=1.$

So $\displaystyle \frac{f(x)-f(2)}{x-2}=\frac{\frac{\sqrt{x-1}}{x-1}-1}{x-2}$

12. ## Re: Composite functions?

Hello, homeylova223!

Evidently, these are from exercises involging Difference Quotients.

How would I multiply this?

. . $\displaystyle \left(x^2+2\Delta x +[\Delta x]^2\right) (x+\Delta x)$

You are in PreCalculus or Calculus
. . and you can't multiply polynomials?

Hint: .$\displaystyle (a+b)^3 \:=\:a^3 + 3a^2b + 3ab^2 + b^3$

Given: .$\displaystyle f(x) \:=\: \frac{1}{\sqrt{x-1}}$

$\displaystyle \text{Find: }\:\frac{f(x)-f(2)}{x-2}$

$\displaystyle f(x) - f(2) \;=\;\frac{1}{\sqrt{x-1}} - \frac{1}{\sqrt{2-1}} \;=\;\frac{1}{\sqrt{x-1}} - 1 \;=\;\frac{1-\sqrt{x-1}}{x-1}$

$\displaystyle \frac{f(x) - f(2)}{x-2} \;=\;\frac{1-\sqrt{x-1}}{(x-1)(x-2)}$

Rationalize the numerator:

. . $\displaystyle \frac{1-\sqrt{x-1}}{(x-1)(x-2)}\cdot\frac{1 + \sqrt{x-1}}{1 + \sqrt{x-1}} \;=\; \frac{1 - (x-1)}{(x-1)(x-2)(1 + \sqrt{x-1})}$

. . $\displaystyle =\;\frac{2-x}{(x-1)(x-2)(1+\sqrt{x-1})} \;=\;\frac{-(x-2)}{(x-1)(x-2)(1+\sqrt{x-1})}$

. . $\displaystyle =\;\frac{-1}{(x-1)(1+\sqrt{x-1})}$

13. ## Re: Composite functions?

Your Algebra skills are supreme I could have never figured that out on my own!