If f, g, h are three functions defined from R to R as follows:
(i) $f (x) = x^{2}$
(ii) $g (x) = s i n x$
(iii) $h (x) = x^{2} + 1$

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Solution

(i) We have,
$f (x) = x^{2}$
Range of $f (x) = R^{+}$ (set of all real numbers greater than or equal to zero)
$= {x ϵ R | x \geq 0}$

(ii) We have,
$g (x) = s i n x$
Range of $g (x) = {x ϵ R : - 1 \leq x \leq 1}$

(iii) We have,
$h (x) = x^{2} + 1$
Range of $h (x) = {x ϵ R : x \geq 1}$

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