Let `f(x)= lnx` & `g(x) =e^x`. if `f_1(x)= f(|x|),f_2(x)=f(|x|),f_3(x)=|f(|x|)|,g_1(x)=1/g(|x|).`

let ( f(x) = 1-|x| , |x| 1 ) g(x)=f(x+1)+f(x-1)

If f(x)=1+2x and g(x) = x/2 , then: (f@g)(x)-(g@f)(x)=

Let f(x) be a function such that f(x)*f(y)=f(x+y),f(0)=1,f(1)=4. If 2g(x)=f(x)*(1-g(x))

If f(x)=x^2 and g(x)=x^2+1 then: (f@g)(x)=(g@f)(x)=

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

Let f:R→R: f(x)=x+1 and g:R→R: g(x)=2x−3 . Find (f−g)(x) .

Let f(x) be a function such that f(x).f(y)=f(x+y) , f(0)=1 , f(1)=4 . If 2g(x)=f(x).(1-g(x))

If f(x)=|x-1| and g(x)=f(f(f(x))) then for x>2,g'(x)=

Let f(x)=x^2+xg^2(1)+g^''(2) and g(x)=f(1).x^2+xf'(x)+f''(x), then find f(x) and g(x).