Question

find domain and range of f(x)=√x^2-100

Answer 1

Answer:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.

solve

x

+

4

=

0

⇒

x

=

−

4

←

excluded value

domain is

x

∈

R

,

x

≠

−

4

(

−

∞

,

−

4

)

∪

(

−

4

,

∞

)

←

in interval notation

let

y

=

x

−

2

x

+

4

to find the range, rearrange making

x

the subject

y

(

x

+

4

)

=

x

−

2

x

y

+

4

y

=

x

−

2

x

y

−

x

=

−

2

−

4

y

x

(

y

−

1

)

=

−

2

−

4

y

x

=

−

2

−

4

y

y

−

1

solve

y

−

1

=

0

⇒

y

=

1

←

excluded value

range is

y

∈

R

,

y

≠

1

or

(

−

∞

,

1

)

∪

(

1

,

∞

)

graph{(x-2)/(x+4) [-10, 10, -5, 5]}