Question

1
Q.36
Find the domain and range of the real function f(x) =
1/4-x²​

Answer 1

Answer:

The square roots are only defined when the expression under the square root is non-negative.

This function is defined when:

36

−

x

2

≥

0

x

2

≤

36

|

x

|

≤

6

−

6

≤

x

≤

6

Answer 2

Answer:

The domain is

x

∈

(

−

2

,

2

)

. The range is

[

1

2

,

+

∞

)

.

Explanation:

The function is

f

(

x

)

=

1

√

4

−

x

2

What'under the

√

sign must be

≥

0

and we cannot divide by

0

Therefore,

4

−

x

2

>

0

⇒

,

(

2

−

x

)

(

2

+

x

)

>

0

⇒

,

{

2

−

x

>

0

2

+

x

>

0

⇒

,

{

x

<

2

x

>

−

2

Therefore,

The domain is

x

∈

(

−

2

,

2

)

Also,

lim

x

→

2

−

f

(

x

)

=

lim

x

→

2

−

1

√

4

−

x

2

=

1

O

+

=

+

∞

lim

x

→

−

2

+

f

(

x

)

=

lim

x

→

−

2

+

1

√

4

−

x

2

=

1

O

+

=

+

∞

When

x

=

0

f

(

0

)

=

1

√

4

−

0

=

1

2

The range is

[

1

2

,

+

∞

)

graph{1/sqrt(4-x^2) [-9.625, 10.375, -1.96, 8.04]}