Let -x-x if x - 0 -x if x - 0- where x - R Does the relation x- y - y - -x- x - define a function- Find its range-

For every value of x there exists a unique value of y Hence the relation (x,y)|y=|x|,x∈R is a functionThis function is always non negative. Its ...

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Standard XII

Mathematics

Definition of Functions

Let |x|=x ...

Question

Let $| x | = {\begin{matrix} x i f & x \geq 0 - x i f & x < 0 \end{matrix}$ , where $x \in R$ Does the relation ${(x, y) | y = | x |, x \in R}$ define a function? Find its range.

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Solution

For every value of $x$ there exists a unique value of $y$
Hence the relation { $(x, y) | y = | x |, x \in R$ } is a function

This function is always non-negative. Its lowest value is equal to $0$ and its value continues to get big.
Hence its $R a n g e \in R$

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Let $| x | = {\begin{matrix} x i f & x \geq 0 - x i f & x < 0 \end{matrix}$ , where $x \in R$ Does the relation ${(x, y) | y = | x |, x \in R}$ define a function? Find its range.

For every value of $x$ there exists a unique value of $y$
Hence the relation { $(x, y) | y = | x |, x \in R$ } is a function

This function is always non-negative. Its lowest value is equal to $0$ and its value continues to get big.
Hence its $R a n g e \in R$