If `f_1(x)=(1)/(x), f_(2) (x)=1-x, f_(3) (x)=1/(1-x)` then find `J(x)` such that `f_(2) o J o f_(1) (x)=f_(3) (x)` (a) `f_(1) (x)` (b) `(1)/(x) f_(3) (x)` (c) `f_(3) (x)` (d) `f_(2) (x)`

If f(x)=(1)/(3)x + 3 , then f^(-1)(x)=

If f_(r)(x), g_(r)(x), h_(r) (x), r=1, 2, 3 are polynomials in x such that f_(r)(a) = g_(r)(a) = h_(r) (a), r=1, 2, 3 and " "F(x) =|{:(f_(1)(x)" "f_(2)(x)" "f_(3)(x)),(g_(1)(x)" "g_(2)(x)" "g_(3)(x)),(h_(1)(x)" "h_(2)(x)" "h_(3)(x)):}| then F'(x) at x = a is ..... .

If f(x)=(x-1)/(x+1) , then show that f(1/x)=-f(x) (ii) f(-1/x)=1/(f(x))

If f(x)=log((1+x)/(1-x))a n dg(x)=((3x+x^3)/(1+3x^2)) , then f(g(x)) is equal to (a) f(3x) (b) {f(x)}^3 (c) 3f(x) (d) -f(x)

If f(x)=(x-1)/(x+1) , then show that f(1/x)=-f(x) (ii) f(-1/x)=-1/(f(x))

If f_1(x)=x ,f_2(x)=1-x ,f_3(x)=1/x ,f_4(x)=1/(1-x),f_5(x)=x/(x-x),f_5(x)=x/(x-1), , f_6(x)=(x-1)/x suppose that f_6(f_m(x))=f_4(x) and f_n(f_4(x))=f_3(x), then m=5 (b) n=5 (c) m=6 (d) n=6

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2)(0)=1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

If f_(1)(x) = 2x + 3, f_(2)(x) = 3x^(2) + 5, f_(3)(x) = x + cos x are defined from R rarr R , then f_(1), f_(2) and f_(3) are

If f(x)=x^3-1/(x^3) , show that f(x)+f(1/x)=0.

If f(x)=x+(1)/(x) , such that f^3 (x)=f(x^(3))+lambdaf((1)/(x)) , then lambda=