Find the range of the following real valued functions:
i) $log ∣ ∣ 4 - x^{2} ∣ ∣$

ii) $\frac{x^{2} - 4}{x - 2}$

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Solution

$1.$ Range of this function is $R$ as range of a log is $R$ .
$2. \frac{(x + 2) (x - 2)}{x - 2}$
$⟹ (x + 2)$
Hence the range is $R$ .

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Similar questions

Find the domain and range of the following real functions:

(i) $f (x) = - | x |$ (ii) $f (x) = \sqrt{9 - x^{2}}$

(i) log ∣ ∣ 4 - x^{2} ∣ ∣

(i i) \frac{x^{2} - 4}{x - 2}

f (x) = x^{2}

f (x) = \sqrt{(x - 1) (3 - x)}

Find the range of each of the following functions:

(i) $f (x) = 2 - 3 x, x ϵ R, x > 0$

(ii) $f (x) = x^{2} + 2, x$ is a real number

(iii) $f (x) = x, x$ is a real number.

Find the range of each of the following functions:

(i) $f (x) = 2 - 3 x, x ϵ R$ and $x > 0$

(ii) $g (x) = x^{2} + 2, x ϵ R$

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