Find whether `f(x)=x^(3)` forms a mapping or not.

Find whether x^(2)/a^(2)+y^(2)/b^(2)=1 forms a mapping or not.

Let f:[-pi//2,pi//2] rarr [-1,1] where f(x)=sinx. Find whether f(x) is one-one or not.

Let f be a function such that f(x+y)=f(x)+f(y) for all xa n dya n df(x)=(2x^2+3x)g(x) for all x , where g(x) is continuous and g(0)=3. Then find f^(prime)(x)dot

The tangent, represented by the graph of the function y=f(x), at the point with abscissa x = 1 form an angle of pi//6 , at the point x = 2 form an angle of pi//3 and at the point x = 3 form and angle of pi//4 . Then, find the value of, int_(1)^(3)f'(x)f''(x)dx+int_(2)^(3)f''(x)dx.

f(x)=x/(1+x^(2)) . Find range of f(x).

Find period of f(x)=tan3x+sin(x/3) .

f(x)=sqrt(9-x^(2)) . find range of f(x).

f : R^(+)to R^(+), f(x)=(log x)/(sqrt(x)) . Find the intervals in which f(x) is increasing or decreasing.

Let X = {1,2,3} and Y = {4,5} . Find whether the following subsets of XxxY are functions form X to Y or not . f = {(1,4),(1,5),(2,4),(3,5)}

Let f: R -{-4/3}rarrR be a function defined as f(x) =(4x)/(3x+4) . The inverse of f is the map g : Range f rarrR - {-4/3} given by