If f(x) is a quadratic expression such that f(x)`gt0 forall x in R`, if g(x) is defined as g(x)=f(x)+f'(x)+f''(x), then prove g(x)`gt 0 forall x in R`.

Let f'(x)gt0 and g'(x)lt0 for all x in R, then

f is a function such that f(x + y) = f(x) .f(y), forall x, y in R , if f(1) = 3, then find sum_(r = 1)^n f(r) .

If f"(x)>0 for all x in R, f'(3)=0,and g(x)=f(tan^2 x-2tan x+4),0

Let g(x)=2f(x/2)+f(x) and f''(x)lt0 " in "0lexle1 , then g(x)

Suppose that f(x) is a quadratic expresson positive for all real x If g(x)=f(x)+f^(prime)(x)+f^(prime prime)(x), then for any real x (where f^(prime)(x) and f^(primeprime)(x) represent 1st and 2nd derivative, respectively). (a) g(x) 0 (c). g(x)=0 (d). g(x)geq0

If f(x) + 2f(1 - x) = x^2 + 2, forall x in R , then f(x) is

A function is defined as f(x) = {(e^x, xle0),(|x-1|, x gt0):} , then f(x) is

int [f(x)g"(x) - f"(x)g(x)]dx is

Let f:R to R and g:R to R is define by f(x)=2x+3 and g(x)=3x-2 , then find (f circ g)(x)

Let f:R to R and g:R to R is define by f(x)=2x+3 and g(x)=3x-2 , then find (g circ f)(x)