The function `y=(2x-1)/(x-2),(x!=2)` (a)is its own inverse (b)decrease at all values of `x` in the domain (c)has a graph entirely above the `x-` axis (d)is unbounded.

The domain of the function cos^(-1)(2x-1) is

The domain of the function f(x)=(log)_(3+x)(x^2-1) is

The number of integral value(s) of a so that the graph of y=16 x^(2)+8(a+5) x-7 a-5 is always above the x -axis is

The area enclosed between the curve y^(2)(2a-x)=x^(3) and the line x=2a above the x-axis is

Statement 1: For all a ,b in R , the function f(x)=3x^4-4x^3+6x^2+a x+b has exactly one extremum. Statement 2: If a cubic function is monotonic, then its graph cuts the x-axis only one.

The function y=2x^2-ln|x| is monotonically increasing for values of x(!=0) satisfying the inequalities____ and monotonically decreasing for values of x satisfying the inequalities_____.

(i) Make a rough sketch of the function y = x^(2) and shade the region under the curve, x-axis and the ordinates at x = 1 and x = 3. (ii) Find the area under the curve y = x^(2) above.

The function defined by f(x)=(x+2)e^(-x) is (a)decreasing for all x (b)decreasing in (-oo,-1) and increasing in (-1,oo) (c)increasing for all x (d)decreasing in (-1,oo) and increasing in (-oo,-1)

Domain of the function y =(x-1)/(x+1) is:

The function f(x)=x(x+4)e^(-x//2) has its local maxima at x=adot Then (a) a=2sqrt(2) (b) a=1-sqrt(3) (c) a=-1+sqrt(3) (d) a=-4