Question

Find domain of real function f(x)=1/x+2​

Answer 1

Answer:

What is the domain and range of the real function f(x)=1/(1-x^2)?

This is a revised answer!

x, y∈R.

Let

y=f(x).

Then

y=11−x2

⟹y=1(1+x)(1−x)

means that

x≠±1

because the denominator cannot be 0.

So the domain of f is

{x|x≠−1 or x≠1}.

To find the range, get x in terms of y.

y=11−x2

⟹y(1−x2)=1  

⟹y−x2y=1

⟹−x2y=1−y

⟹x2y=y−1

⟹x2=y−1y=yy−1y

=1−1y.

So clearly,

y≠0.

Then because it is a square,

x2≥0.

This means that

1−1y≥0.

Then either

y<0

because that makes

−1y>0,

or

y≥1

because that makes

1y

a unit fraction that is smaller than 1.

So,

y<0 or y≥1.

The range is

{y|y<0 or y≥1}.

Step-by-step explanation:

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