Question

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

Answer 1

Someone help me out please

Answer 2

@Hero Can you help me please?

Answer 3

@phi

Answer 4

@ganeshie8

Answer 5

@amistre64

Answer 6

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?

Answer 7

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

Answer 8

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

Answer 9

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)

Answer 10

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

Answer 11

almost.

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

Answer 12

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

Answer 13

one thing at a time.

what do you get after dividing by -8
?

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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
\[ y = \frac{± \sqrt{x}+7}{8} \\ y = \frac{7± \sqrt{x}}{8}
\]

Answer 18

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

Answer 19

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

Answer 20

so its not a function

Answer 21

correct

Answer 22

Okay. Thank you so much for helping me out!

Answer 23

yw