Question

Find the domain of definition and the range of the following function:
$y=\log (5x^2-8x+4)$

Answer 1

$y=log({5x}^2-8x+4)$

For $y$ to be real and defined,

${5x}^2-8x+4>0$

${5x}^2-8x+4>0\forall x\in R$

Therefore, domain of $y$ is $x\in R$

Minimum value of ${5x}^2-8x+4$ is at $x=\frac{-(-8)}{2\left(5\right)}=\frac{4}{5}$

At, $x=\frac{4}{5},{5x}^2-8x+4=\frac{4}{5}$

Therefore range of $y$ is $\left[log\right(\frac{4}{5}),\infty ).$