The function y = cos x is one - to - one and onto in the interval $[\frac{- π}{2}, \frac{π}{2}]$

True

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False

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Solution

The correct option is B False
If a function is one-to-one, a line drawn parallel to x axis, must intersect the graph at exactly one point. This is not the case for cos x in $[\frac{- π}{2}, \frac{π}{2}]$ . So cos x is not one-to-one function.

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Similar questions

[\frac{- π}{2}, \frac{π}{2}]

f : (- 1, 1) \to B

f (x) = t a n^{- 1} \frac{2 x}{1 - x^{2}}

(0, π / 2)

(0, π / 2)

- \frac{π}{2}, \frac{π}{2}

R

f (x) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} x + a^{2} \sqrt{2} s i n x, & 0 \leq x < \frac{π}{4} x c o t x + b, & \frac{π}{4} \leq x < \frac{π}{2} b s i n 2 x - a c o s 2 x, & \frac{π}{2} \leq x \leq π \end{matrix}

[0, π]

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