There are exactly two distinct linear functions, ______ and ______, which map [-1,1] onto [0,2].

There are exactly two distinct linear functions, ______ and ______, which map [-1,1] onto [0,4].

If fa n dg are two distinct linear functions defined on R such that they map [-1,1] onto [0,2] and h : R-{-1,0,1}vecR defined by h(x)=(f(x))/(g(x)), then show that |h(h(x))+h(h(1/x))|> 2.

Let A be a set of n distinct elements. Then the total number of distinct function from AtoA is ______ and out of these, _____ are onto functions.

For the equation |[1,x,x^2],[x^2, 1,x],[x,x^2, 1]|=0, There are exactly two distinct roots There is one pair of equation real roots. There are three pairs of equal roots Modulus of each root is 2

If the equation sin ^(2) x - k sin x - 3 = 0 has exactly two distinct real roots in [0, pi] , then find the values of k .

If f is a linear function and f(2)=4,f(-1)=3 then find f(x)

Let l_(1) and l_(2) be the two skew lines. If P, Q are two distinct points on l_(1) and R, S are two distinct points on l_(2) , then prove that PR cannot be parallel to QS.

The number of 3xx3 matrices A whose entries are either 0or1 and for which the system A[x y z]=[1 0 0] has exactly two distinct solution is a. 0 b. 2^9-1 c. 168 d. 2

If set of values a for which f(x)=a x^2-(3+2a)x+6, a!=0 is positive for exactly three distinct negative integral values of x is (c , d] , then the value of (c^2 + 4|d|) is equal to ________.

If x^(4) + 2kx^(3) + x^(2) + 2kx + 1 = 0 has exactly tow distinct positive and two distinct negative roots, then find the possible real values of k.