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) and g(x) are two real functions such that f(x)+g(x)=e^(x) and f(x)-g(x)=e^(-x) , then

Let f and g be differentiable functions such that: xg(f(x))f\'(g(x))g\'(x)=f(g(x))g\'(f(x))f\'(x) AA x in R Also, f(x)gt0 and g(x)gt0 AA x in R int_0^xf(g(t))dt=1-e^(-2x)/2, AA x in R and g(f(0))=1, h(x)=g(f(x))/f(g(x)) AA x in R Now answer the question: f(g(0))+g(f(0))= (A) 1 (B) 2 (C) 3 (D) 4

If f(x) and g(x) are functions such that f(x + y) = f(x) g(y) + g(x) f(y), then in |(f(alpha),g(alpha),f(alpha+theta)),(f(beta),g(beta),f(beta+theta)), (f(lambda),g(lambda),f(lambda+theta))| is independent of

If f (x) is a function such that f (x) + f''(x) =0 and g (x)= (f (x))^(2) +(f' (x))^(2) and g (3) =8, then g (8)=

If f(x) be a function such that f(-x)= -f(x),g(x) be a function such that g(-x)= -g(x) and h(x) be a function such that h(-x)=h(x) , then choose the correct statement: I. h(f(g(-x)))=-h(f(g(x))) II. f(g(h(-x)))=f(g(h(x))) III. g(f(-x))=g(f(x))

f(x) and g(x) are two differentiable functions in [0,2] such that f"(x)=g"(x)=0, f'(1)=2, g'(1)=4, f(2)=3, g(2)=9 then f(x)-g(x) at x=3/2 is

Identify the type of the functions: f(x)={g(x)-g(-x)}^(3)

Let f:R to R and g:R to R be differentiable functions such that f(x)=x^(3)+3x+2, g(f(x))=x"for all "x in R , Then, g'(2)=

Suppose that g(x)=1+sqrt(x) and f(g(x))=3+2sqrt(x)+xdot Then find the function f(x)dot