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Question

Find the domain and range of the following real function: (i) f ( x ) = –| x | (ii)

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Solution

(i)

The given function is f( x )=| x |.

It is known that,

| x |={ x,x0 x,x<0

So, the given function becomes,

f( x )=| x |={ x,x0 x,x<0

The given function is defined for xR, so, the domain of f( x ) is R.

Since, the range of the given function is all real numbers except positive real numbers, so, the range of f( x ) is ( ,0 ].

(ii)

The given function is f( x )= 9 x 2 .

The given function is defined for all real numbers that are less than or equal to 3 and greater than or equal to 3.

So, the domain of f( x ) is,

{ x:3x3 } or [ 3,3 ].

As the value of f( x ) lie between 0 and 3, for any value of x such that, 3x3, so, the range of the given function is,

{ x:0x3 } or [ 0,3 ].


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