Question

domain of the function f(x) = 1/(x²-x)​

Answer 1

The domain is

x

∈

R

. The range is

y

∈

(

0

,

1

]

Explanation:

The denominator is

=

1

+

x

2

∀

x

∈

R

,

1

+

x

2

>

0

Therefore,

The domain of

f

(

x

)

is

x

∈

R

To determine the range, proceed as follows

y

=

1

1

+

x

2

y

(

1

+

x

2

)

=

1

y

+

y

x

2

=

1

y

x

2

=

1

−

y

x

2

=

1

−

y

y

x

=

√

1

−

y

y

The range of

f

(

x

)

is the domain of

x

(

1

−

y

y

)

>

0

y

∈

R

*

+

1

−

y

≥

0

y

≤

1

Therefore,

The range is

y

∈

(

0

,

1

]

graph{1/(1+x^2) [-11.25, 11.25, -5.625, 5.625]}

Answer link

warning: it is by google, and i think it is wrong

Answer 2

Answer:

It is [-Infinity, 0) U (0,1) U (1, infinity]

Step-by-step explanation:

For f (x)

$= \frac{1}{ {x}^{2} - x }$

• f (x) should not be simultaneously infinity, and then simultaneously convergent,

So x²- x can't be 0.

Which means that x can't be 0, or 1.

That's all.