The domain and range of $y = f (x) = cos (log x)$ are

D : (0, \infty); R : (- 1, 1)

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D : (0, \infty); R : [0, 1]

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D : (0, \infty); R : [- 1, 1]

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D : (0, \infty); R : (0, 1)

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Solution

The correct option is C $D : (0, \infty); R : [- 1, 1]$
Given, $y = cos (log x)$

For this function to be defined, $log x$ should be defined $\Rightarrow x > 0$
Thus $D; (0, \infty)$
also we know $- 1 \leq cos θ \leq 1$
$\Rightarrow$ Range $: [- 1, 1]$

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The domain and range of y = sinx is

f (x) = \frac{x}{|x|}

A = [- 1, 1], B = [- 1, 1], C = [0, \infty)

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R_{2} = {(x, y) \in A \times C : x^{2} + y^{2} = 1}

f (x) = cos (\sqrt{x})

$R a n g e o f t h e f u n c t i o n y = \frac{2^{x} - 2^{- x}}{2^{x} + 2^{- x}} i s$

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