Given f(x) = `log_a(x)` passing through the point(3:1) Determine the value of a. Determine the equation of `y=f^(-1)(x)`

If the curve y=f(x) passing through the point (1,2) and satisfies the differential equation xdy+(y+x^(3)y^(2))dx=0 ,then

IF f(x)=log(3x+1), then the value of f'' (1) is-

The graph of the function y = f(x) passing through the point (0, 1) and satisfying the differential equation (dy)/(dx) + y cos x = cos x is such that

The graph of the function y = f(x) passing through the point (0, 1) and satisfying the differential equation (dy)/(dx) + y cos x = cos x is such that

f (x)= max |2 sin y-x| where y in R then determine the minimum value of f (x).

If f'(x)=x-1, the equation of a curve y=f(x) passing through the point (1,0) is given by

If y=f(x)=(2x+3)/(5x-a) , then determine the value of a so that x = f(y).

If a curve y=f(x) passes through the point (1,-1) and satisfies the differential equation, y(1+x y)dx""=x""dy , then f(-1/2) is equal to: