pre-calculus

[skeletonslayer89]

I need help with the following, find the difference quotient g(x+h)-g(x)/h. g(x)=3/x

 

[Steven G]

To receive help we need to know where you are stuck. So please share your work with us so we can offer real help.

I suspect that you meant to write [g(x+h)-g(x)]/h and not g(x+h)-g(x)/h.

Hint: 1st calculate g(x+h). Remember that the rule for g is to take whatever is in the parenthesis put it in the denominator and put a 3 in the numerator. Give it a try.

 

[Deleted member 4993]

I need help with the following, find the difference quotient g(x+h)-g(x)/h. g(x)=3/x

Does your problem look like:

\(\displaystyle \frac{g(x+h) - g(x)}{h} \)

or

\(\displaystyle g(x+h) - \frac{g(x)}{h} \)

 

[Steven G]

Does your problem look like:

\(\displaystyle \frac{g(x+h) - g(x)}{h} \)

or

\(\displaystyle g(x+h) - \frac{g(x)}{h} \)

What do you think?

 

[HallsofIvy]

What they probably meant was \(\displaystyle \frac{g(x+ h)- g(x)}{h}\)
but what they wrote was \(\displaystyle g(x+ h)- \frac{g(x)}{h}\) so I think Subhotosh Kahn's question is perfectly reasonable.

skeletonslayer89, if you are asking about the difference quotient \(\displaystyle \frac{g(x+ h)- g(x)}{h}\) with \(\displaystyle g(x)= \frac{3}{x}\) then \(\displaystyle g(x+ h)= \frac{3}{x+ h}\) and \(\displaystyle g(x+ h)- g(x)= \frac{3}{x+ h}- \frac{3}{x}= \frac{3x}{x(x+h)}- \frac{3(x+ h)}{x(x+ h)}= \frac{3x- 3x- 3h}{x(x+ h)}= -\frac{3h}{x(x+h)}\).

 

[Steven G]

What they probably meant was \(\displaystyle \frac{y(x+ h)- y(x)}{h}\)
but what they wrote was \(\displaystyle y(x+ h)- \frac{y(x)}{h}\) so I think Subhotosh Kahn's question is perfectly reasonable.

The real question is if Subhotosh Khan is reasonable? I think he is!

 

[Deleted member 4993]

What they probably meant was \(\displaystyle \frac{g(x+ h)- g(x)}{h}\)
but what they wrote was \(\displaystyle g(x+ h)- \frac{g(x)}{h}\) so I think Subhotosh Kahn's question is perfectly reasonable.

skeletonslayer89, if you are asking about the difference quotient \(\displaystyle \frac{g(x+ h)- g(x)}{h}\) with \(\displaystyle g(x)= \frac{3}{x}\) then \(\displaystyle g(x+ h)= \frac{3}{x+ h}\) and \(\displaystyle g(x+ h)- g(x)= \frac{3}{x+ h}- \frac{3}{x}= \frac{3x}{x(x+h)}- \frac{3(x+ h)}{x(x+ h)}= \frac{3x- 3x- 3h}{x(x+ h)}= -\frac{3h}{x(x+h)}\).

I was 99.539% sure that the original question involved the expression:

\(\displaystyle \frac{g(x+ h)- g(x)}{h}\)

But I wanted the original poster to be aware of the fact that - s/he posted an ambiguous problem!

 

[HallsofIvy]

The real question is if Subhotosh Khan is reasonable? I think he is!

Well, I can't speak for he, himself, only for what he posts here.

 

[Steven G]

I was 99.539% sure that the original question involved the expression:

\(\displaystyle \frac{g(x+ h)- g(x)}{h}\)

But I wanted the original poster to be aware of the fact that - s/he posted an ambiguous problem!

I stated their probable error in the post before you.