Question

..Let f: IR→IR be defined by f(x) = 1 - 1x| then the range of fis​

Answer 1

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GiveN :

Function f is defined,

$\rightsquigarrow \sf \: f : R \to R$

$\rightsquigarrow \sf f(x) = 1 - |x|$

To FinD :

$\sf \rightsquigarrow \: Range \: \: of \: \: function$

SolutioN :

$\tt \star \: \: \: { \underline{\underline{Domain \: \: of \: \: function (D_f) \: : }}}$

• For any real value of x function is defined to R
• Hence,
• ${ \underline {\boxed {\sf x \in \: R}}}$

$\tt \star \: \: \: { \underline{\underline{Range \: \: of \: \: function (R_f) \: : }}}$

• we Know,
• $\sf \: |x| \geqslant 0$
• Substituting +ve and -ve value of x we will always get +ve value of f(x) . For of non positive-negative number, [0] we will get 0 as an output. Hence, highest value of f(x) is 1 [ when x= 0 ]

• ${\underline{\boxed{\sf \:f(x) \in \: [ \: 1 \: , \: \infty \: )}}}$

ConcepT BoosteR :

→ For better understanding let's have a look in the GRAPHICAL REPRESENTATION of this function

${ \underline{ \underline{ \mathbb{GRAPH \: \: IS \: \: ATTACHED \: \: IN \: \: PHOTO}}}}$

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HOPE THIS IS HELPFUL...

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