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The range of sgn(2^x) + sgn(Ix-5I) is ?
Asked by hrajput0322 | 11 Jun, 2019, 12:06: PM
answered-by-expert Expert Answer
s g n space x equals open curly brackets table row cell 1 comma space space space x greater than 0 end cell row cell 0 comma space space space x equals 0 end cell row cell negative 1 comma space x less than 0 end cell end table close 2 to the power of x space i s space a l w a y s space g r e a t e r space t h a n space 0 space i. e. space 2 to the power of x greater than 0 space f o r space a l l space x element of R rightwards double arrow s g n left parenthesis 2 to the power of x right parenthesis equals 1 vertical line x minus 5 vertical line equals 0 space f o r space x equals 5 space a n d space vertical line x minus 5 vertical line greater than 0 space f o r space a l l space x element of R minus open curly brackets 5 close curly brackets rightwards double arrow s g n left parenthesis 2 to the power of x right parenthesis equals 0 space o r space 1 rightwards double arrow s g n left parenthesis 2 to the power of x right parenthesis plus s g n left parenthesis vertical line x minus 5 vertical line right parenthesis equals 1 space o r space 2 space rightwards double arrow s g n left parenthesis 2 to the power of x right parenthesis plus s g n left parenthesis vertical line x minus 5 vertical line right parenthesis element of left curly bracket 1 comma 2 right curly bracket H e n c e comma space t h e space r a n g e space o f space s g n left parenthesis 2 to the power of x right parenthesis plus s g n left parenthesis vertical line x minus 5 vertical line right parenthesis space i s space left curly bracket 1 comma 2 right curly bracket.
Answered by Renu Varma | 11 Jun, 2019, 12:52: PM

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