Let `f(x)=tanxa n dg(f(x))=f(x-pi/4),` where `f(x)a n dg(x)` are real valued functions. Prove that `f(g(x))="tan` `((x+1)/(x+1))dot`

Let f be a real-valued function such that f(x)+2f((2002)/x)=3xdot Then find f(x)dot

Find the value of x for which function are identical. f(x)=xa n dg(x)=1/(1//x)

If f(x)=(a x^2+b)^3, then find the function g such that f(g(x))=g(f(x))dot

If f(x)=|x-2|a n dg(x)=f[f(x)],t h e ng^(prime)(x)= ______ for x>2

Let f(x)a n dg(x) be two continuous functions defined from RvecR , such that f(x_1)>f(x_2)a n dg(x_1) f(g(3alpha-4))

Let f(x)=x^(2) and g(x)=2x+1 be two real functions. Find (f+g) (x), (f-g) (x), (fg) (x), (f/g) (x) .

Let f(x)=a^(x)(a gt 0) be written as f(x)=f_(1)(x)+f_(2)(x), " where " f_(1)(x) is an function and f_(2)(x) is an odd function. Then f_(1)(x+y)+f_(1)(x-y) equals

Let f(x)=x^2-2x ,x in R ,a n dg(x)=f(f(x)-1)+f(5-f(x))dot Show that g(x)geq0AAx in Rdot

If f(x)={1-|x|,|x|lt=1 0,|x|>1'a n dg(x)=f(x-1)+f(x+1), find the value of int_(-3)^3g(x)dxdot

Ifint(x^4+1)/(x^6+1)dx=tan^(-1)f(x)-2/3tan^(-1)g(x)+C ,t h e n both f(x)a n dg(x) are odd functions f(x) is monotonic function f(x)=g(x) has no real roots int(f(x))/(g(x))dx=-1/x+3/(x^3)+c