Consider three functions `f(x)=x^2-4x, g(x)=x+5, h(x)=x-12`. On the basis of above information, answer the following question:
Number of integral values which are not in the range of `(g(f(x)))/(h(f(x)))` is:
A) One
B) Two
C) Three
D) Four

If f(x)=|x-3|+2|x-1| and g(x)=-2x^(2)+3x-1 On the basis of above information answer the following questions: Minimum value of f(x) is

Let f(x)={x;x =0 and g(x)+{x^(2);x<-1 and 2x+3;-1<=x<=1 and x ; On the basis of above information,answer the following questions Range of f(x) is

Let there are two functions defined of f(x)="min"{|x|,|x-1|,|x+1+] and g(x)="min"{e^(x),e^(-x)} on the basis of above information answer the following question: Number of solutions of f(x)=g(x) in the interval [0,1] is

If f(x)=(x-2)|x-4| sgn(x)AA x in R (Where sgn( x ) denotes signum function) On the basis of above information answer the following questions: f(x) is monotonically increasing in interval-

If f(x)=(x-2)|x-4| sgn(x)AA x in R (Where sgn( x ) denotes signum function) On the basis of above information answer the following questions: f(x) is monotonically increasing in interval-

If f_r(x),g_r(x),h_r(x),r=1,2,3 are differentiable function and y=|(f_1(x), g_1(x), h_1(x)), (f_2(x), g_2(x), h_2(x)),(f_3(x), g_3(x), h_3(x))| then dy/dx= |(f\'_1(x), g\'_1(x), h\'_1(x)), (f_2(x), g_2(x), h_2(x)),(f_3(x), g_3(x), h_3(x))|+ |(f_1(x), g_1(x), h_1(x)), (f\'_2(x), g\'_2(x), h\'_2(x)),(f_3(x), g_3(x), h_3(x))|+|(f_1(x), g_1(x), h_1(x)), (f_2(x), g_2(x), h_2(x)),(f\'_3(x), g\'_3(x), h\'_3(x))| On the basis of above information, answer the following question: Let f(x)=|(x^4, cosx, sinx),(24, 0, 1),(a, a^2, a^3)| , where a is a constant Then at x= pi/2, d^4/dx^4{f(x)} is (A) 0 (B) a (C) a+a^3 (D) a+a^4

consider the function f(X) = 3x^(4)+4x^(3)-12x^(2) The range of values of a for which f(x) = a has no real

Consider a function f(x)=x^(x), AA x in [1, oo) . If g(x) is the inverse function of f(x) , then the value of g'(4) is equal to