Suppose f is defined from R- -1-1 - as f x - x 2 -1 x 2 -1 where R is the set of real number- Then statement which does not hold is

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Definition of Function

Suppose f i...

Question

Suppose $f$ is defined from $R \to [- 1, 1]$ as $f (x) = \frac{x^{2} - 1}{x^{2} - 1}$ where $R$ is the set of real number. Then statement which does not hold is

f i s m a n y o n e o n t o

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f i n c r e a s e s f o r x > 0 a n d d e c r e a s e f o r x < 0

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m i n i m u m v a l u e i s n o t a t t a i n e d e v e n t h o u g h f i s b o u n d e d

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t h e a r e a i n c l u d e d b y t h e c u r v e y = f (x) a n d t h e l i n e y = 1 i s π s q . u n i t s .

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Solution

The correct option is B $f i s m a n y o n e o n t o$
so, $f (x)$ is constant function.

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Suppose f is defined from R→[−1,1] as f(x)=x2−1x2−1 where R is the set of real number. Then statement which does not hold is

The correct option is B f is many one ontoso, f(x) is constant function.

Suppose $f$ is defined from $R \to [- 1, 1]$ as $f (x) = \frac{x^{2} - 1}{x^{2} - 1}$ where $R$ is the set of real number. Then statement which does not hold is

The correct option is B $f i s m a n y o n e o n t o$
so, $f (x)$ is constant function.