1 f(x) = χ_ 2 at x = 1. for 1

If f(x) = 1 + x + x^(2) + …… for |x| lt 1 then show that f^(-1)(x) = (x-1)/(x) .

If f(1) = 1, f'(1) = 3, then the derivative of f(f(x))) + (f(x))^(2) at x = 1 is

If f(1) = 1, f'(1) = 3, then the derivative of f(f(x))) + (f(x))^(2) at x = 1 is

If f(x) = 4x - x^2 , then f (a + 1) - f( a - 1) =

If f(x)=x for 0<=x<(1)/(2),f(x)=1f or x=(1)/(2) and f(x)=1- for (1)/(2)<<1 then at x=(1)/(2) the function is

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...... .

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...... .

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(x) is continuous at x=1 , where f(x)=(log_(2)2x)^(1/(log_(2)x) , for x!=1 , then f(1)=