The relation f is defined by

The relation g is defined by

Show that f is a function and g is not a function.

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Solution

The relation f is defined as

It is observed that for

0 ≤ x < 3, f(x) = x²

3 < x ≤ 10, f(x) = 3x

Also, at x = 3, f(x) = 3² = 9 or f(x) = 3 × 3 = 9

i.e., at x = 3, f(x) = 9

Therefore, for 0 ≤ x ≤ 10, the images of f(x) are unique.

Thus, the given relation is a function.

The relation g is defined as

It can be observed that for x = 2, g(x) = 2² = 4 and g(x) = 3 × 2 = 6

Hence, element 2 of the domain of the relation g corresponds to two different images i.e., 4 and 6. Hence, this relation is not a function.

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g (x) = \{\begin{cases} x^{2}, & 0 \leq x \leq 2 \\ 3 x, & 2 \leq x \leq 10 \end{cases}

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The relation f is defined by

$f (x) = {\begin{matrix} x^{2}, & 0 \leq x \leq 2 3 x, & 3 \leq x \leq 10 \end{matrix}$

The relation g is defined by

$g (x) = {\begin{matrix} x^{2}, & 0 \leq x \leq 3 3 x, & 2 \leq x \leq 10 \end{matrix}$

Show that f is a function and g is not a function.

The function f is defined by
$f (x) = {\begin{matrix} x^{2}, 0 \leq x \leq 3 3 x, 3 \leq x \leq 10 \end{matrix}$
The relation g is defined by
$g (x) = {\begin{matrix} x^{2}, 0 \leq x \leq 2 3 x, 2 \leq x \leq 10 \end{matrix}$
Show that f is a function and g is not a function.

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The relation f is defined by The relation g is defined by Show that f is a function and g is not a function.

The relation f is defined by

The relation g is defined by

Show that f is a function and g is not a function.