anonymous
  • anonymous
Use the following three steps to find and simplify the difference quotient of the function f(x)=\frac{1}{x-6}.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
f(x) = 1/x-6
anonymous
  • anonymous
I believe I do the correct work but for the last two steps it says I am wrong.
anonymous
  • anonymous
@ganeshie8

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
@Hero
Jhannybean
  • Jhannybean
The difference quotient: \(\dfrac{f(x+h)-f(x)}{h}\) So let's begin by finding \(f(x+h)\) first. Wherever you see an x, replace it with \(x+h\)
anonymous
  • anonymous
1/x-6 = 1/(x+h)-6
anonymous
  • anonymous
then i'm suppose to subtract it by f(x)
Jhannybean
  • Jhannybean
Alright, now we plug it in to the formula. And you are already given \(f(x)\).
anonymous
  • anonymous
1/(x+h)-6 - 1/x = -h-6/x(x+h)-6
Jhannybean
  • Jhannybean
\[\frac{f(x+h)-f(x)}{h} = \frac{\dfrac{1}{x+h-6}-\dfrac{1}{x-6}}{h}\]
Jhannybean
  • Jhannybean
When I find a common denominator, I multiply both the denominators of the fraction together.
Jhannybean
  • Jhannybean
\[=\frac{\dfrac{x-6 -(x+h-6)}{(x-6)(x+h-6)}}{h}\]
Jhannybean
  • Jhannybean
Now let's simplify both the numerator and denominator.
anonymous
  • anonymous
isn't the top suppose to be -h
anonymous
  • anonymous
-h/(x+h-6)(x-6)
anonymous
  • anonymous
then -h/(x+h-6)(x-6)/h
Jhannybean
  • Jhannybean
Yep, you're on track. That's what I got too. \[=\frac{\dfrac{x-6-x-h+6}{(x-6)(x+h-6)}}{h} = -\frac{\dfrac{h}{(x-6)(x+h-6)}}{h}\]
Jhannybean
  • Jhannybean
Now remember the rule of dividing fractions? \(\dfrac{\dfrac{a}{b}}{c} \iff \dfrac{a}{bc}\)
anonymous
  • anonymous
its -h^2/(x+h-6)(x-6)
Jhannybean
  • Jhannybean
We're going to apply this rule to our simplified function. We multiply \((x-6)(x+h-6)\) with \(h\).
Jhannybean
  • Jhannybean
Not exactly.
Jhannybean
  • Jhannybean
\[ -\frac{\dfrac{h}{(x-6)(x+h-6)}}{h} = -\frac{h}{h(x-6)(x+h-6)}\]Therefore both the h's cancel out.
Jhannybean
  • Jhannybean
\[-\frac{\cancel{h}}{\cancel{h}(x-6)(x+h-6)}\]
anonymous
  • anonymous
ahhh i understand
anonymous
  • anonymous
it says the bottom is not correct
anonymous
  • anonymous
nevermind
Jhannybean
  • Jhannybean
when you think of a fraction in the form \(\dfrac{\dfrac{a}{b}}{c}\) think of \(\dfrac{a}{b} \cdot \dfrac{1}{c} = \dfrac{a}{bc} \)
anonymous
  • anonymous
i forgot the - lol
Jhannybean
  • Jhannybean
Ahh, good good.

Looking for something else?

Not the answer you are looking for? Search for more explanations.