Question

. Find the domain of the real function x+1/ x−2 , x is not equal to 2

Answer 1

Answer:

he 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]}

Step-by-step explanation:

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