Question

write the domain of f(x)= 1/x²-1 ​

Answer 1

$\large\underline\purple{\bold{Solution :- }}$

$\tt :  ⟼ \: f(x) = \dfrac{1}{ {x}^{2} - 1 }$

$\tt :  ⟼ \: f(x) = \dfrac{1}{(x - 1)(x + 1)}$

$\bf\implies \:Domain \: of \: f(x) \: is \: x \: \epsilon \: R - \{ - 1 \: , \: 1 \}$

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Note :- The domain of a function is the set of all possible inputs for the function.

Answer 2

√X^2–1 is not equal to 0 , X^2–1 is not equal to 0 also, (X+1)(X-1) is not equal to 0 & X is not equal to -1 & 1 .

For root function to be defined…….

X^2–1>=0…(1)

(X+1)(X-1)>=0...(2)

i.e. X lies between (-infinite, -1)U(1,infinite)

Domain (f) ={X|X€R, X€(-infinite, -1)U(1,infinite)}

Rewriting function,

Y=1/√X^2–1

Y^2=1/X^2–1

X^2–1=1/Y^2

X^2=(Y^2+1)/Y^2

X=√Y^2+1/Y

for this to be defined Y can't be equal to 0 and for all values of Y, √Y^2+1>0

Range (f)={Y|Y€R}=R-{0}

hope it's helpful