`f(x)={ax^2+bx+c, |x| > 1 x+1, |x| <= 1.` If `f(x)` is continuous for all values of x, then;

f(x)={ax^(2)+bx+c,|x|>1x+1,|x|<=1 If f(x) is continuous for all values of x, then;

If f(x)=ax^(2)+bx+c and f(x + 1) = f(x) + x + 1, then determine the values of a and b.

If f(x)=ax^(2)+bx+c and f(x - 1) = f(x) + 2x + 1. then find the values of a and b.

If f(x) = ax^(2) + bx + x and f(2) = 1, f(3) = 6, f(-1) = 10, then find the value of f'(1).

If f(x) = ax^2 + bx + c find a, b so that f(x + 1) = f(x) + x + 1 may hold identically.

Suppose f(x) = {{:(a+bx "," x lt 1),(4 "," " "x=1),(b-ax "," x gt 1):}

Let for a != a_1 != 0 , f(x)=ax^2+bx+c , g(x)=a_1x^2+b_1x+c_1 and p(x) = f(x) - g(x) . If p(x) = 0 only for x = -1 and p(-2) = 2 then the value of p(2) .