Question

give the domain of f(x)=(x+1)^5+1 and the domain of f^-1(x)

Answer 1

domain of f(x) is all real numbers
domain of f(x)^-1 is all real numbers since the power is odd.

Answer 2

first is all real numbers, second is all real numbers not equal to 0, because it takes values of x and turns them into 1/0 which is undefined

Answer 3

it turns x into 1/x, which in the case of 0 would be 1/0, I should have said

Answer 4

domain for the second one is all real nos except -2

Answer 5

\[f ^{-1}=(\sqrt[5]{x-1})-1\]
Domain is all reall numbers since the fifth root exist for all real numbers

Answer 6

i think hes asking for the reciprocal of f(x) and not the inverse

Answer 7

i believe xon is correct, its all real numbers for both f and f^-1, you can take 5th roots of any number, positive or negative

Answer 8

so what is f^-1(0)

Answer 9

using xon's equation:
\[f^{-1}(0) = \sqrt[5]{(0-1) } - 1 = -1-1 = -2\]

Answer 10

f^-1(0)=(-1)^(1/5)-1
f^-1(0)=-1-1
f^-1(0)=-2

Answer 11

I assumed it was two seperate unrelated equations, asking for domain of each

Answer 12

ahh, now I see, no = sign in second

Answer 13

i guess it really depends on what the poster means by f^-1

Answer 14

it is the inverse

Answer 15

cool, that what I thought. go with xon's answer.

Answer 16

yep, sorry for the confusion

Answer 17

its all good, nothing like some mathematical debating to shake things up :)

Answer 18

ya, if you wanted the reciprocal, then it should be 1/f(x) or f(x)^-1 because the inverse is defined as f^-1(x). 1/f(x) is not always equal to f^-1(x)