If `A={x : x in R, (-pi)/(2) le x le (pi)/(2)}, B={y : y in R, -1 le y le 1}`, then show that the function `f: A to B ` defined as `f(x)=sin x , x in A ` is one-one onto function.

Given A = {x : (pi)/(6) le x le (pi)/( 3)} and f(x) = cos x - x ( 1+ x ) . Find f (A) .

If f : {x : -1 le x le 1} rarr {x : -1 le x le 1} , then which is/are bijective ?

Let |f (x)| le sin ^(2) x, AA x in R, then

For -(pi)/(2)le x le (pi)/(2) , the number of point of intersection of curves y= cos x and y = sin 3x is

y - 2x le 1, x + y le 2, x ge 0, y ge 0

Let f: X rarr Y be a function defined by f(x) = a sin ( x + pi/4 ) + b cosx + c. If f is both one-one and onto, then find the set X and Y

Let f(x)=(x^(2)+2)/([x]),1 le x le3 , where [.] is the greatest integer function. Then the least value of f(x) is

Let f(x) = {{:(x^(2) + 3x",", -1 le x lt 0),(-sin x",", 0 le x lt pi//2),(-1 - cos x",", (pi)/(2) le x le pi):} . Draw the graph of the function and find the following (a) Range of the function (b) Point of inflection (c) Point of local minima

The area of the region {(x,y): xy le 8,1 le y le x^(2)} is :

Consider a function defined in [-2,2] f (x)={{:({x}, -2 le x lt -1),( |sgn x|, -1 le x le 1),( {-x}, 1 lt x le 2):}, where {.} denotes the fractional part function. The total number of points of discontinuity of f (x) for x in[-2,2] is: