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Find the domain of each of the following functions given by (i) f(x)=x|x| (ii) f(x)=\frac{x^{3}-x+3}{x^{2}-1}
CBSE | Class 11 | Maths | NCERT Exemplar | Relations and Functions
Find the domain of each of the following functions given by (i) f(x)=x|x| (ii) f(x)=\frac{x^{3}-x+3}{x^{2}-1}

Solution:

(i)

f(x)=x|x|

As per the question,

It is known that x and |x| are defined for all real values.

As a result, the domain of f=R

(ii)

f(x)=\frac{\left(x^{3}-x+3\right)}{x^{2}-1}

As per the question,

For real value of

\begin{array}{l} x^{2}-1 \neq 0 \\ \Rightarrow(x-1)(x+1) \neq 0 \\ \Rightarrow x-1 \neq 0 \text { or } x+1 \neq 0 \\ \Rightarrow x \neq 1 \text { or } x \neq-1 \end{array}

As a result, the domain of f=R-\{-1,1\}

i

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