A. `2^x` + `2^(f(x))` = 2

If f(x) is periodic with periot 't' such that f(2x + 3) + f(2x+7) = 2 , then the coefficient of m^-24 in the expansion of (m+b/m^3)^(4t) 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

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...... .

Find the range of (a) f(x) = x^(2) + 2x + 4 (b) f(x) = 1+x -x^(2)

Describe the motion of a particle acted upon by a force (i) F= -2(x - 2)^(3) (ii) F= -2(x - 2)^(2) (iii) F= -2(x - 2)

Find the range : (i) f(x) = 2x^(2) (ii) f(x) = -x^(2)

If f (x) = x^(4) + 2x^(3) , them lim_(x to 2) (f(x) - f(2))/(x - 2) is equal to

If 2^(f(x)) = (2+x)/(2-x), x in (-2, 2) and f(x) = lambda f((8x)/(4+ x^(2))) then value 'lambda' will be

Statement-1 : For real values of x and y the relation y^(2) = 2x - x^(1) - 1 represents y as a function of x. Statement-2 : If f(x) = log (x-2)(x-3) and g(x) = log(x-2) + log (x-3) then f=g Statement-3 : If f(x+2) = 2x-5 then f(x) = 2x-9.

Let f(x)= 2^(2x−1) and ϕ(x) = −2^x+2xlog2 . If f'(x)>ϕ'(x), then value of x is-