- Thread starter
- #1
Continuous and rational implies that \(f(x)\) is a constant.if $f(x)$ be a continous and assumes only rational values so that $ f(2010) =1. $ then roots of
the equation $f(1)x^2 + 2f(2)x + 3f(3) =0$ are
If \(f(x)\) is continuous it satisfies the intermediate value principle, that is \(f(x)\) takes on all values between \(f(a)\) and \(f(b)\) for any distinct reals \(a\) and \(b\).means $x^2+2x+3=0\Leftrightarrow (x+1)^2+2>0\forall x\in \mathbb{R}$
Means no real Roots.
but I did not understand the line if $f(x)$ is Conti. and assume only rational values .then it must be Constant
Thanks