Question

PLEASE HELP
f(x)=(x-11)^2 where x
11 years ago

Answer 1

Hey Miss Britt c:

Step 1: Rename your \(\Large\rm f(x)\) to \(\Large\rm y\).

Step 2: Your \(\Large\rm x\)'s and \(\Large\rm y\)'s switch places.

Step 3: Solve for your \(\Large\rm y\).

Answer 2

\[\Large\rm f(x)=(x-11)^2\]
Here is step 1:\[\Large\rm y=(x-11)^2\]
Here is step 2:\[\Large\rm x=(y-11)^2\]

Answer 3

From here, we want to isolate our \(\Large\rm y\).
Hmm it's being squared...
What can we do to "undo" the squaring?
What is the inverse operation of squaring?

Answer 4

square root

Answer 5

Mmmm good good good, yah let's use that.

Answer 6

\[\Large\rm \pm\sqrt{x}=y-11\]We usually end up with a plus/minus when taking the root of a square. I dunno if it's going to matter here though, mm thinking.

Answer 7

cant be positive because of restriction

Answer 8

if x <= 11, then y >= 0 for the original function f(x)

the domain and range swaps because x and y have swapped. So the domain of the inverse is x >= 0 and the range for the inverse is y <= 11

Answer 9

ah good point, both of you c: hehe

Answer 10

\[\Large\rm \sqrt{x}=y-11\]

Answer 11

After you've finished solving for y, replace it with the notation, \(\Large\rm f^{-1}(x)\).

Answer 12

because the range is y <= 11, this means negative y outputs are possible. So you go for the negative form of the square root (not the positive)

Answer 13

Woops, I forgot to write the new restriction >.< Sorry bout that.

Answer 14

Ah i forgot to put the negative on the root as well :(
Oh boy, it's not my night...

Answer 15

oh thats what i did wrong, i forgot the negative sign too

Answer 16

Ah :)

Answer 17

hmm, how do i find the domain

Answer 18

[11, inf) ?

Answer 19

If you look back at what Jim was saying,
Our `old range` becomes our `new domain`.

Our range was, \(\Large\rm (0,\infty)\).
So that becomes our domain.

Answer 20

ohh okay

Answer 21

thanks!

Answer 22

Here is a graph of the functions, just in case you were curious :)
https://www.desmos.com/calculator/hamwlcgtll
The orange is the f(x), half of a parabola (because of the x restriction).
Blue is the inverse function.