Question

If the set of real roots of the function f(x)is (-2,1,3), find the set of real roots for f(3x)

Answer 1

Suppose the function if \(f(x)=x-1\), which has root \(x=1\). If we replace \(x\) with \(3x\), then we have \(f(3x)=3x-1\), which has root \(x=\dfrac{1}{3}\).

This means the set of roots is multiplied by a factor of \(\dfrac{1}{3}\), and so the roots of \(f(3x)\) are \(\left\{-\dfrac{2}{3},\dfrac{1}{3},1\right\}\).