List of practice Questions

For all real values of x, the range of the function \(f(x) =\frac{ x^2+2x+4}{2x^2+4x+9}\) is

If \(f(x)=x^2−7x\) and \(g(x)=x+3\), then the minimum value of \(f(g(x))−3x\) is

Let \(f(x)=x^2+ax+b\) and \(g(x)=f(x+1)-f(x-1)\). If \(f(x)≥0\) for all real \(x\), and \(g(20)=72\), then the smallest possible value of \(b\) is

If \(f(x+y)=f(x)f(y)\) and \(f(5)=4\), then \(f(10)-f(-10)\) is equal to

If f \((5+x) = f (5-x)\) for every real x, and \(f(x)=0\) has four distinct real roots, then the sum of these roots is