sorryimfrankie
  • sorryimfrankie
Inverse of a function
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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sorryimfrankie
  • sorryimfrankie
I already know the answer, I just want to understand it
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♪Chibiterasu
  • ♪Chibiterasu
Well the first thing we do to make this easier is replace f(x) with y.
♪Chibiterasu
  • ♪Chibiterasu
And then you switch x and y.

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sorryimfrankie
  • sorryimfrankie
Right, got it :)
♪Chibiterasu
  • ♪Chibiterasu
\[y = 12 - \frac{ 3 }{ 4 }x~---> x = 12 - \frac{ 3 }{ 4 }y\]
♪Chibiterasu
  • ♪Chibiterasu
And then you solve for y to isolate it again.
sorryimfrankie
  • sorryimfrankie
That's where I'm stuck, I'm not sure where to start
♪Chibiterasu
  • ♪Chibiterasu
Well here we want to get rid of the fraction because who doesn't hate fractions. The denominator is 4 so we multiply both sides by 4.
♪Chibiterasu
  • ♪Chibiterasu
\[x \times 4 = 12 - \frac{ 3 }{ 4 }y \times 4\]
sorryimfrankie
  • sorryimfrankie
So I have 4x = 12 - 3y?
♪Chibiterasu
  • ♪Chibiterasu
We are multiply the entire side by 4, so the 4 will apply to ALL terms. the 4x is correct and so is the 3y, but we apply it to the 12 as well.
sorryimfrankie
  • sorryimfrankie
Okay, wasn't sure about that, alright, one sec, let me write it down
♪Chibiterasu
  • ♪Chibiterasu
np
sorryimfrankie
  • sorryimfrankie
Alright so we have 4x = 48 - 3y so now we do what?
♪Chibiterasu
  • ♪Chibiterasu
We move more terms. We can remove the 3 on the y. 3y is being multipled so we divide 3 on both sides.
♪Chibiterasu
  • ♪Chibiterasu
Ack, hold on. The frist thing we had to do was subtract 12 on both sides. Woops. x = 12 - 3/4y x - 12 = -(3/4)y 4(x - 12) = -3y
sorryimfrankie
  • sorryimfrankie
I thought that was going in the wrong direction lol. no worries
♪Chibiterasu
  • ♪Chibiterasu
So do you understand so far? Just to make sure since I made a mistake there. :x
sorryimfrankie
  • sorryimfrankie
Yes, I got it so far :)
sorryimfrankie
  • sorryimfrankie
So now we divide both sides by 3, correct?
♪Chibiterasu
  • ♪Chibiterasu
Alright. 4(x - 12) = -3y Now we can pass on the -3. We divide it on both sides.
♪Chibiterasu
  • ♪Chibiterasu
Yes. =)
sorryimfrankie
  • sorryimfrankie
Sweet, you got me to the right answer. I appreciate it :)
♪Chibiterasu
  • ♪Chibiterasu
It would be -4/3(x - 12) If you want to avoid confusion you can just multiply the inverse. From (-3/4)y you can change it to -4/3 and attach it to the x. SAme exact thing, less confusion. Dividing a fraction is the same and multiply by its inverse!
♪Chibiterasu
  • ♪Chibiterasu
Np, also make sure that you use \[f^{-1}(x)\] to replace the y we changed at the beginning
♪Chibiterasu
  • ♪Chibiterasu
to indicate :)
sorryimfrankie
  • sorryimfrankie
Right, I'm just practicing stuff so I can get better at math, thanks again for helping so much :)

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