Evaluate the difference quotient for the given function

[shaun_m_smith]

I just need a little help starting this problem. I have completed similar problems but, this one is causing me some difficulties.
f(x)=(1/x) , [ { f(x) - f(a) } / (x-a) ] . I guess my problem is that this is the first one of these for me with two functions or are they?

Thanks to anyone who may reply.

 

[shaun_m_smith]

So, I think I am messing this up from the very start.

f(x)= (1/x) , [ {(f(x) - f(a) } / (x-a) ]
find f(x) = (1/x) ???
Simplifiy f(x) - f(a)= is f(a) the same as f(x)

That is basically the clarification I need. It has been years since I have last done this type of work. I could use a point in the right direction.

Thanks again to anyone that replies.

 

[skeeter]

f(x) = 1/x ... f(a) = 1/a

[f(x) - f(a)]/(x - a) =

[(1/x) - (1/a)]/(x - a) =

get a common denominator and combine the two fractions in the numerator ...

[(a - x)/(ax)]/(x - a) =

[-(x - a)/(ax)]/(x - a) = -1/(ax)

 

[shaun_m_smith]

Well ,I was in fact messing it up from the start. I was confused about the value of f(a) thank you.
I do have an additional conceptual question. what is the relationship between f(x) and f(a)? Are they the same function?

 

[stapel]

what is the relationship between f(x) and f(a)? Are they the same function?

The name of the function or formula is "f(x)", where "f(x)" means the exact same thing as "y" "in terms of x".

The "f(a)" means you've plugged "a" in for "x" in the formula for "f(x)". :wink:

Eliz.