Let a relation f defined on 0- - as fx - -1 - 1x- Then which among the following is true

F( 1)=2 is not true as 1 is not an element in domain of relation. f(x) = |1 1x| For x = 1 f(x) = |1 11| = 0 But, the co domain of relation is (0, ∞) which ...

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Let a relatio...

Question

Let a relation $f$ defined on $(0, \infty)$ as $f (x) = ∣ ∣ ∣ 1 - \frac{1}{x} ∣ ∣ ∣$ . Then which among the following is true

f (- 1) = 2

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f

is many-one function

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f

is one-one function

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Relation

f

is not a function

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Solution

The correct option is D Relation $f$ is not a function
$f (- 1) = 2$ is not true as $- 1$ is not an element in domain of relation.
$f (x) = ∣ ∣ ∣ 1 - \frac{1}{x} ∣ ∣ ∣$
For $x = 1$
$f (x) = ∣ ∣ ∣ 1 - \frac{1}{1} ∣ ∣ ∣ = 0$
But, the co-domain of relation is $(0, \infty)$ which is not including $0.$
So, relation $f$ is not a function.

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Let a relation f defined on (0,∞) as f(x)=∣∣∣1−1x∣∣∣. Then which among the following is true

The correct option is D Relation f is not a functionf(−1)=2 is not true as −1 is not an element in domain of relation. f(x)=∣∣∣1−1x∣∣∣ For x=1 f(x)=∣∣∣1−11∣∣∣=0 But, the co-domain of relation is (0,∞) which is not including 0. So, relation f is not a function.

Let a relation $f$ defined on $(0, \infty)$ as $f (x) = ∣ ∣ ∣ 1 - \frac{1}{x} ∣ ∣ ∣$ . Then which among the following is true