Question

State a restricted domain for f(x)=| x-5 | such that f(x) has an inverse function. Do NOT write the inverse function.

Answer 1

I don't understand what this question is asking . Please explain? :) thx

Answer 2

for a function to have an inverse it must be a one-to-one function For the above to have an inverse we must restrict the domain.
lets see what the function | x-5 | gives us for some values of x

x | x-5 |

-1 6
-2 7
11 6
12 7


so, you see, with a domain that includes all those numbers the function is not one-to-one That is why we need to restrict the domain

Answer 3

so can you state a restricted domain for this function?

Answer 4

I need to see the complete steps. How do you restrict domain?

Answer 5

you can restrict the domain by observing the values of x and corresponding values of f(x)
lets look at some more values of x
x = 4 f(x) =| 4- 5 | = | -1 | = 1
x = 6 f(x) = | 6-5 | = 1

x = 5 gives us f(x) = 0

so if we restrict the domain to x >=5 we have a one to one function

Answer 6

so f(x) now has an inverse when the domain is x>= 5