Intro to functions

Is f(x) = (1-x^2)^-1 a total function? If it isnt, what is its domain?
Ty for all the help

Original post by phillipJFries

Is f(x) = (1-x^2)^-1 a total function? If it isnt, what is its domain?
Ty for all the help

Look at the definition of what it means for

f

to be a total function.

Is

(1-x^2)^{-1}

defined for all

x \in \mathbb{R}

Ahh the graph has asymptotes at 1 and -1, so it is not.
Therefore the domain is x>1, x<-1, -1>x<1 i assume? Is this the correct notation?

(edited 6 years ago)

Original post by phillipJFries

Ahh the graph has asymptotes at 1 and -1, so it is not.
Therefore the domain is x>1, x<-1, -1>x<1 i assume? Is this the correct notation?

Not sure how

-1>x<1

in this situation since that just means

x<-1

, thus no new info.

The correct notation would be to say

x \in \mathbb{R} \setminus \{ -1, 1 \}

(-\infty, -1) \cup (-1, 1) \cup (1, \infty)

x<-1

-1<x<1

x>1

(edited 6 years ago)

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