SATHEE: Functions 1 Question 1

Functions 1 Question 1

1. The domain of the definition of the function $f (x) = \frac{1}{4 - x^{2}} + \log_{10} (x^{3} - x)$ is

(2019 Main, 9 April II)

(a) $(- 1, 0) \cup (1, 2) \cup (3, \infty)$

(b) $(- 2, - 1) \cup (- 1, 0) \cup (2, \infty)$

(d) $(1, 2) \cup (2, \infty)$

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Answer:

Correct Answer: 1. (c)

Solution:

Given function $f (x) = \frac{1}{4 - x^{2}} + \log_{10} (x^{3} - x)$

For domain of $f (x)$

$\begin{array}{lrl} 4 - x^{2} \neq 0 \Rightarrow x \neq \pm 2 \\ and & x^{3} - x > 0 \\ \Rightarrow & x (x - 1) (x + 1) > 0 \end{array}$

From Wavy curve method,

$x \in (- 1, 0) \cup (1, \infty)$

From Eqs. (i) and (ii), we get the domain of $f (x)$ as $(- 1, 0) \cup (1, 2) \cup (2, \infty)$ .

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Functions 1 Question 1

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1. The domain of the definition of the function $f (x) = \frac{1}{4 - x^{2}} + \log_{10} (x^{3} - x)$ is