Adi3
  • Adi3
Will medal please help. consider g(n) = -12-2n/3. Find g^-1(n)
Mathematics
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Adi3
  • Adi3
Will medal please help. consider g(n) = -12-2n/3. Find g^-1(n)
Mathematics
katieb
  • katieb
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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.

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Adi3
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Jhannybean
  • Jhannybean
Is your function : \(g(n) = \dfrac{-12-2n}{3}\)?
Adi3
  • Adi3
yes
Adi3
  • Adi3
we need to find the inverse.
Jhannybean
  • Jhannybean
So first graph it to see whether it's a one-to-one function, and it is. \[y = \frac{-12-2n}{3}\]Switch y and n \[n=\frac{-12-2y}{3}\]Now lets solve for y.
Jhannybean
  • Jhannybean
I let my function \(g(n) = y\)
Jhannybean
  • Jhannybean
What function do you get when you resolve for y?
Adi3
  • Adi3
3n + 12 = -2y
Jhannybean
  • Jhannybean
Good, and when you isolate y?
Adi3
  • Adi3
that's where i reached till, i don't know what to do after that
Jhannybean
  • Jhannybean
To isolate the variable y, what do you have to do to each side of the equation?
Adi3
  • Adi3
divide by 2 i guess
Jhannybean
  • Jhannybean
-2, and yes, you were partially right.
Adi3
  • Adi3
so 3n + 12/-2 = y
Jhannybean
  • Jhannybean
(3n + 12)/ -2 = y * It helps when you put parenthesis () around the numerator and denominator
Adi3
  • Adi3
can I ask one more question please????
Jhannybean
  • Jhannybean
We can simplify that function a bit by dividing both terms in the numerator by -2. ((3n)/-2) +(12/-2) = y
Jhannybean
  • Jhannybean
Sure, I can try helping.
Adi3
  • Adi3
ok, find the inverse of the equation f(x) = \[-\frac{ 4 }{ 7 }x - \frac{ 16 }{ 7 }\]
Jhannybean
  • Jhannybean
\[y=\frac{-4x-16}{7}\]Same process, we switch x and y. \[x=\frac{-4y-16}{7}\] and now we resolve for y.
Adi3
  • Adi3
7x +16 = -4x
Adi3
  • Adi3
right?
Jhannybean
  • Jhannybean
-4y*
Adi3
  • Adi3
ohh yeah
Jhannybean
  • Jhannybean
7x + 16 = -4y and now we've got to isolate y, just like before.
Adi3
  • Adi3
\[\frac{ 7x+16 }{ -4 }\]
Jhannybean
  • Jhannybean
That's right, and after resolving for y, we relabel it as \(f^{-1}(x)\)
Adi3
  • Adi3
ok, can i ask further questions if i have doubt in them please?
Jhannybean
  • Jhannybean
Sure, but im logging off for a while, although good luck on learning this!`
Adi3
  • Adi3
when will you come back

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