Question

1.find the domain of the following function 1/(x^2-1)(x+3)

Answer 1

Answer:

Solution :-

(i)f(x)=x

2

Domian =R Range =R

+

(ii)f(x)=

(x−1)(3−x)

Domian : (x−1)(3−x)≥0⇒(x−1)(x−3)≤0

Domain : xϵ[1,3]

Range :-

Let y=

(x−1)(3−x)

⇒y

2

=(x−1)(3−x)

⇒y

2

=3x−x

2

−3+x⇒−x

2

+4x−3

⇒x

2

−4x+3+y

2

=0

⇒x=

2

4±

16−4(3+y

2

)

Now above equation is defined for

16−4(3+y

2

)=0

⇒4≥(3+y

2

)

⇒1≥y

2

⇒1−y

2

≥0

⇒(1−y)(1+y)≥0

Range : yϵ(−∞,1]∪[1,∞)