If `f(x)=x^(2)-4x+14,` g(x) = x - 1, q(x) = x - 3 and f(x) = g(x) q(x) + r(x), then find r(x).

If f(x)=x^(2)+ax-2a^(2)+1,g(x)=x-a,q(x)=x+2aandf(x)=g(x)*q(x)+r(x) then r(x) =

If g (x) is the inverse of f (x) and f(x)=(1)/(1+x^(3)) , then find g(x) .

If f(x) = (x - 7) q(x) + r(x), where f(x)=x^(3)-7x^(2)+1 and r(x) = 1, then find q(x).

If f: R^+ to R , f(x) + 3x f(1/x)= 2(x+1),t h e n find f(x)

Use the Factor Theorem to determine whether g (x) is factor of f(x) in each of the following cases: (i) f (x) = 5x ^(3) + x ^(2)-5x -1, g (x)=x +1 (ii) f (x) = x ^(3) + 3x ^(2) + 3x +1 , g(x) =x +1 (iii) f (x) =x ^(3) - 4x ^(2) +x + 6, g (x) =x -2 (iv) f (x) = 3x ^(3) - 20x + 12, g (x) = 3x -2 (v) f (x) = 4x ^(3) + 20 x ^(2) + 33 x +18, g (x) =2x +3

Find gof and fog, if (i) f (x) = |x| and g (x) = |5x - 2| (ii) f (x) = 8x ^(3) and g (x) = x ^(1/3).

If f(x)=e^x and g(x) =log_(e)x, then find (f+g)(1) and fg(1).

Let f(x)=sqrt(x-2) , g(x)= sqrt(5-x) find f(x)+g(x), f(x)-g(x), f.g., (f/g)

If f(x)=sinx, g(x)=x^2 and h(x)=log x, find h[g{f(x)}].

Let f and g be two functions defined by f(x)=(x)/(x+1), g(x) =(x)/(1-x) . If ( f o g ) ^(-1) (x) is equal to kx, then find the value of k.