Show that f- R - R- given by fx-x-x- is neither one-one nor onto-

We have, f(x) = x nbsp; nbsp;[x] Injection test: f(x) = 0 for all x #8712; Z So, f nbsp;is a many one function. Surjection test: Range (f) = [0, ...

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Geometrical Explanation of Rolle's Theorem

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Question

Show that f : R $\to$ R, given by f(x) = x $-$ [x], is neither one-one nor onto.

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Solution

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f : R \to R

f (x) = \frac{x}{x^{2} + 1}

\forall x \in R

f : R \to R, f (x) = \frac{x}{x^{2} + 1}

f : R \to R

f (x) = \frac{x}{x^{2} + 1}

x \in R

Let the function $f : R \to R$ be defined by $f (x) = c o s x, \forall x \in R$ . Show that $f$ is neither one-one nor onto.

f : R \to R

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x < 0

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