Question

The function f is given by f (x) = e^(x–11) –8.
(a) Find f –1(x).
(b) Write down the domain of f –1(x).

Answer 1

-1 = inverse...

Answer 2

Kinda confused

Answer 3

sorry! not sure.. this might help tho, http://www.zweigmedia.com/RealWorld/calctopic1/inverses.html

Answer 4

\[y=e^{x-11}-8\\\text{we want to solve for x in terms of y}\\\text{add 8 to both sides}\\y+8=e^{x-11}\\\text{take natural log of both sides}\\ln(y+8)=ln(e^{x-11})=(x-11)ln*(e)=x-11\\so\\ln(y+8)=x-11\\\text{add 11 to both sides}\\ln(y+8)+11=x\\\text{now switch the x's with y's so that we have a function of x}\\y=ln(x+8)-11\]

Answer 5

@trace60 let me know if this makes sense.

Answer 6

n/m, @zzr0ck3r answered it in the exact same way I would :)

Answer 7

But wait whats the domain? =S

Answer 8

the domain depends on the definition of the function, but I'm guessing it is all real numbers for codomain.

having said that, is there any value of x we cant put in our final equation?

Answer 9

Domain of original function = range of inverse function

Range of original function = domain of inverse function

So start with the original function - find it's domain and range.

Answer 10

No, there are no values for x and thank you

Answer 11

What's the range of f (x) = e^(x–11) –8 ? this will be your domain of the inverse.

Answer 12

The range of f(x) is f(x)>=-8, so if it were going to have an inverse it must be onto and 1-1 its codomain. so the domain of the inverse, while having no problems on the real line, will have a restricted domain.

Answer 13

Would a table of values be necessary in the finding of the domain?

Answer 14

No, what's the minimum possible value of f (x) = e^(x–11) –8?

think of it like this... if e^(x-11) is really really really small, what's f(x) equal to?

Answer 15

Finding the domain and range has never been my cup of tea so like =/ ...still not with you on that one

Answer 16

If e^(x-11) is zero, then what's f (x) = e^(x–11) –8 equal to?

Answer 17

Note that e^(x-11) can never be a negative number, it can only be almost zero, or positive.

Answer 18

If e^(x-11) is zero, then f(x) = 0 - 8

Answer 19

So then f(x) =0? *squints eyes*

Answer 20

Try again :P

Answer 21

8

Answer 22

Try one more time...

Answer 23

-.-

Answer 24

0-8 is not positive 8

Answer 25

So -8 is the minimum possible value for the range.

What's the max possible value for f (x) = e^(x–11) –8 ?

Answer 26

Or, is there one?

Answer 27

So there's no limit, so the range is from y=-8 to infinity.

That becomes the domain of your inverse, so the domain of x is...?

Answer 28

Oops i deleted that.

So your range for y is from -8 to infinity

This becomes your domain for the inverse function.

Answer 29

Thank you