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Properties of Periodic Function

x^2+x+1 is on...

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x^2+x+1 is one-one function,why?

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Q. Find the domain and range of

f (x) = x^{2} / (1 + x^{2})

(x real ). Is the function one-to-one?

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

Show that function is neither one-one, nor onto.

Q. Check whether

f : R \to R

be a function defined by

f (x) = \frac{x^{2} + 2 x + 5}{x^{2} + x + 1}

is one-one or not.

Q. The function

f (x) = x - | x - x^{2} |, - 1 \leq x \leq 1

is continuous on the interval

Q. The function

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

is monotonically decreasing on

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