[" The number of solution of the "],[" equation "a^(f(x))+g(x)=0," where "a>0" ,"],[g(x)#0" and "g(x)>=(1)/(2)" is "]

The no. of solutions of the equation a^(f(x)) + g(x)=0 where a>0 , and g(x) has minimum value of 1/2 is :-

The no.of solutions of the equation a^(f(x))+g(x)=0 where a>0, and g(x) has minimum value of 1/2 is :

The no. of solutions of the equation a^(f(x)) + g(x)=0 where a>0 , and g(x) has minimum value of 1/2 is :- (a) One (b) Two (c) Infinitely many (d) Zero

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...... .

Let f(x) be a non-positive continuous function and F(x)=int_(0)^(x)f(t)dt AA x ge0 and f(x) ge cF(x) where c lt 0 and let g:[0, infty) to R be a function such that (dg(x))/(dx) lt g(x) AA x gt 0 and g(0)=0 The number of solution(s) of the equation |x^(2)+x-6|=f(x)+g(x) is/are

Let f(x) be a non-positive continuous function and F(x)=int_(0)^(x)f(t)dt AA x ge0 and f(x) ge cF(x) where c lt 0 and let g:[0, infty) to R be a function such that (dg(x))/(dx) lt g(x) AA x gt 0 and g(0)=0 The number of solution(s) of the equation |x^(2)+x-6|=f(x)+g(x) is/are

An equation of the form (f(x))^((1)/(2n))=g(x) equivalent to the system g(x)>=0;f(x)=g^(2n)(x)