The function y -cos x is one - to - one and onto in the interval -2- -2-A- TrueB- False

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Standard XII

Mathematics

Basic Inverse Trigonometric Functions

The function ...

Question

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

Q. The function y = cos x is one - to - one and onto in the interval

[\frac{- π}{2}, \frac{π}{2}]

Q. Let

f : (- 1, 1) \to B

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

, then f is both one - one and onto when B is the interval

Q. Show that f(x) = tan⁻¹ (sin x + cos x) is a decreasing function on the interval (π/4, π/2).

Q. From[

- \frac{π}{2}, \frac{π}{2}

] which of the following is one-one onto function defined in

R

Sketch the graph of the following functions on the same scale.
(i) y=cos x and y =cos $(x - \frac{π}{4})$
(ii) y=cos 2 x and y = cos2 $(x - \frac{π}{4})$
(iii) y =cos x and y = cos $(\frac{x}{2})$

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The function y = cos x is one - to - one and onto in the interval [−π2,π2]

The correct option is B FalseIf 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 [−π2,π2]. So cos x is not one-to-one function.

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

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.