1. ## pre-calculus/functions help

hello all,

question:

$\displaystyle f(x)=1/x$ evaluate $\displaystyle f(x)-f(a)/x-a$

thank you

2. $\displaystyle f(x)-f(a)/x-a = 1/x-(1/a)*(1/x)-a = f(x)(1-1/a)-a$

or you can write it as

$\displaystyle f(x)-f(a)/x-a = 1/x-(1/a)*(1/x)-a = (a-1)/(a*x)-a$

3. Originally Posted by str33tl0rd
hello all,

question:

$\displaystyle f(x)=1/x$ evaluate $\displaystyle f(x)-f(a)/x-a$

thank you
There is nowhere to start. It looks like you've got the slope of a secant line through a hyperbola (assuming that you meant to include parentheses).

Do you have any more instruction?

4. thank you for the help guy, but it seems like that wasn't the answer =|

i think i have miswritten the question, i'll retry:

if $\displaystyle f(x)=1/x$
evaluate
$\displaystyle [f(x)-f(a)]/(x-a)$

and the answer is supposed to be: $\displaystyle -1/ax$

i need a working out, thank you very much all you guys and girls

5. Originally Posted by str33tl0rd
thank you for the help guy, but it seems like that wasn't the answer =|

i think i have miswritten the question, i'll retry:

if $\displaystyle f(x)=1/x$
evaluate
$\displaystyle [f(x)-f(a)]/(x-a)$

and the answer is supposed to be: $\displaystyle -1/ax$
$\displaystyle \frac{\frac{1}{x} - \frac{1}{a}}{x-a}$

get a common denominator for the two terms in the numerator and combine into a single fraction ...

$\displaystyle \frac{\frac{a-x}{ax}}{x-a}$

now finish it

6. thank you, thats the step i got up to:

$\displaystyle \frac{\frac{a-x}{ax}}{x-a}$

and i continued as follows, correct me if i am wrong:
$\displaystyle \frac{a-x}{ax*(x-a)}$
expanding:
$\displaystyle \frac{a-x}{ax(sqr)-a(sqr)x}$

and here is where i get stuck, don't know how to continue or simply that, thanks again

7. Originally Posted by str33tl0rd
thank you, thats the step i got up to:

$\displaystyle \frac{\frac{a-x}{ax}}{x-a}$

and i continued as follows, correct me if i am wrong:
$\displaystyle \frac{a-x}{ax*(x-a)}$

do not $\displaystyle \to$ expand

now, what does $\displaystyle \textcolor{red}{\frac{a-x}{x-a}}$ = ???
...

8. thank you very much...