Question

find the domain of f(x)=(x+1)(x+2)/(x-1)(x-2)

Answer 1

Answer:

Domain

:

x

∈

R

Range

:

f

(

x

)

∈

[

−

√

2

+

1

2

,

√

2

−

1

2

]

Explanation:

Considering that all real values of

x

will give a non-zero value for

x

2

+

1

, we can say that for

f

(

x

)

, domain =

x

∈

R

For range, we need the maximum and minimum.

f

(

x

)

=

x

−

1

x

2

+

1

f

'

(

x

)

=

(

x

2

+

1

)

−

2

x

(

x

−

1

)

(

x

2

+

1

)

2

=

x

2

+

1

−

2

x

2

+

2

x

x

2

+

1

=

−

x

2

+

2

x

+

1

x

2

+

1

The maximum and minimum values occur when

f

'

(

x

)

=

0

x

2

−

2

x

−

1

=

0

x

=

2

±

√

(

−

2

)

2

−

4

(

−

1

)

2

x

=

2

±

√

8

2

=

2

±

2

√

2

2

=

1

±

√

2

Now, we input our

x

values into

f

(

x

)

:

1

+

√

2

−

1

(

1

+

√

2

)

2

+

1

=

√

2

−

1

2

1

−

√

2

−

1

(

1

−

√

2

)

2

+

1

=

−

√

2

+

1

2

f

(

x

)

∈

[

−

√

2

+

1

2

,

√

2

−

1

2

]

Step-by-step explanation:

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