OpenStudy (anonymous):

For the function f(x)=(7-8x)^2 find f^-1. Determine whether f^-1 is a function.

4 years ago
OpenStudy (anonymous):

Someone help me out please

4 years ago
OpenStudy (anonymous):

@Hero Can you help me please?

4 years ago
OpenStudy (anonymous):

@phi

4 years ago
OpenStudy (anonymous):

@ganeshie8

4 years ago
OpenStudy (anonymous):

@amistre64

4 years ago
OpenStudy (phi):

the way people find the inverse function is "swap" x and y in the original equation, then solve for y in other words, start with \[ f(x)=(7-8x)^2 \\ y= (7-8x)^2 \] now "swap" x and y: \[ x= (7-8y)^2 \] now solve for y the first step is take the square root of both sides. what do you get?

4 years ago
OpenStudy (anonymous):

\[\sqrt{x}=7-8y?\]

4 years ago
OpenStudy (anonymous):

Would I add the seven to the inside or the outside of the sqrt

4 years ago
OpenStudy (phi):

looks good, so far. if you remember "order of operations" , Parens, Exponents, multiply/divide, add/subtract. square roots are like exponents. I would add -7 to both sides as the next step (outside the square root)

4 years ago
OpenStudy (anonymous):

so would it be \[\frac{ \sqrt{x}-7 }{ 8 }=y\]

4 years ago
OpenStudy (phi):

almost. \[ \sqrt{x} -7 =7-8y - 7\\ \sqrt{x} -7 = -8y\] now divide both sides by -8 (not just 8)

4 years ago
OpenStudy (anonymous):

But the only answers it has are \[\frac{ 7\pm \sqrt{x} }{ 8 }\] and whether or not its a function

4 years ago
OpenStudy (phi):

one thing at a time. what do you get after dividing by -8 ?

4 years ago
OpenStudy (anonymous):

\[\frac{ \sqrt{x}-7 }{ -8 }\]

4 years ago
OpenStudy (phi):

ok, now multiply top and bottom by -1 (-1/-1 = 1 , so this does not change the value, just how it looks)

4 years ago
OpenStudy (anonymous):

So then its \[\frac{ \sqrt{x}+7 }{ 8 }\]?

4 years ago
OpenStudy (phi):

bottom is ok. -1( sqr(x) -7) is -sqr(x) +7 \[ \frac{-\sqrt{x}+7}{8} \] but the square root has two answers. For example: 2*2 = 4 and -2*-2 = 4 so +2 and -2 are sqrt(4). we show this by writing \[\pm \sqrt{4} \] in other words, your equation is \[ y = \frac{- ± \sqrt{x}+7}{8} \] that simplifies to \[ y = \frac{± \sqrt{x}+7}{8} \\ y = \frac{7± \sqrt{x}}{8} \]

4 years ago
OpenStudy (anonymous):

Oh okay but how do we tell if its a function?

4 years ago
OpenStudy (phi):

a function has only one y value for an x value but that ± in front of the square root gives you 2 different answers for y

4 years ago
OpenStudy (anonymous):

so its not a function

4 years ago
OpenStudy (phi):

correct

4 years ago
OpenStudy (anonymous):

Okay. Thank you so much for helping me out!

4 years ago
OpenStudy (phi):

yw

4 years ago