If `f(x)=x^2+bx+c` and `f(2+t)=f(2-t)` for all real number t, then which of the following is true?

Let f (x) =ax ^(2) + bx+ c,a gt = and f (2-x) =f (2+x) AA x in R and f (x) =0 has 2 distinct real roots, then which of the following is true ?

Let f(x)=(1-x)^(2)sin^(2)x+x^(2) for all x in IR, and let g(x)=int_(1)^(x)((2(t-1))/(t-1)-ln t)f(t) dt for all x,in(1,oo). Which of the following is true?

Consider the quadratic function f(x)=ax^(2)+bx+c where a,b,c in R and a!=0, such that f(x)=f(2-x) for all real number x. The sum of the roots of f(x) is

If f(x) = int_(0)^(x) e^(t^(2)) (t-2) (t-3) dt for all x in (0, oo) , then

If f and g are real fucntions defined by f(x)=x^(2)+7 and g (x) 3x+5 Then , find each of the following . f(3)+g(-5) (ii) f((1)/(2)) xxg(14) (iii) f(-2)+g(-1) (iv) f(t)-f(-2) (v) (f(t)-f(5))/(t-5)if t ne5

If f(t) = 1/(t^(2)-t-6) and t = 1/(x-2) then the values of x which make the function f discontinuous are

Given a function f(x) such that It is integrable over every interval on the real line,and f(t+x)=f(x), for every x and a real t Then show that the integral int_(a)^(a+t)f(x)dx is independent of a .