Question

How do you find the domain of the function f and of its inverse function f-1? f(x) = cos(x - 2) + 7

Answer 1

Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

Answer 2

Domain = "all valid inputs for x". Or to say it another way "what values of x will NOT give you 1/0 or square root of a negative or a log of a number less than or equal to 0?"

Answer 3

the domain is all real numbers. this function is just about as not one to one as you can get, so it does not have an inverse.

Answer 4

if you choose you can restrict the domain of cosine to say \[(0,\pi)\] and then it will be one to one and have an inverse. perhaps that is what they are asking you to do, to restrict the domain to give an inverse

Answer 5

thank you both. I didnt know it was possible for a function not to have an inverse.

Answer 6

in which case you would say "restrict the domain to \[(2,\pi+2)\] and then this thing would be one to one

Answer 7

Have you tried graphing the function?

Answer 8

i dont really know how to graph it

Answer 9

sure. if the function is not one to one then it does not have a function for an inverse. in some cases you can restrict the domain of your function to make it one to one. for example \[f(x)=cos(x)\] is certainly not one to one but if you restrict it for \[(0,\pi)\] then it is.

Answer 10

TO GRAPH ANYTHING

1) go to http://www.wolframalpha.com
2) type " plot y = cos(x-2) + 7

There it is. :)

Answer 11

if you do that in your case here, your function says :subtract 2, take the cosine, then add 7. your inverse would say to do the opposite things in the opposite order : subtract 7, take the inverse cosine, add 2.

Answer 12

Thank you mathteacher1729 and satellite73!!!!! a lot!
I'll try doing the other problem like this and if i need help I'll let u know

Answer 13

i will write out a possible inverse for you if you like. it would just do exactly the opposite of what this one does, as i wrote in english above

Answer 14

\[f^{-1}(x)=cos^{-1}(x-7)+2\]

Answer 15

the domain of your original function would be
\[(2, \pi+2)\] and the range would be [6,8] making the domain of your inverse function [6,8] and your range [2, pi+2)

Answer 16

okay and then the inverse would be (-2, pi -2)?

Answer 17

I'm sorry..I'm slow in math

Answer 18

hello?