Question

Consider the function $y=f(x)=x^2-6x+5$
Range of the function $y=\ln (f(x))$ is

• A. $R$
• B. $[1,\infty )$
• C. $[0,\infty )$
• D. $[-4,\infty )$

Answer 1

Answer: (A)

$f(x)=x^2-6x+5$
$f^{\prime }(x)=2x-6=0$

$x=3$
also $f^{\prime \prime }(x)=2$
$f(x){]}_{\min .}=9-18+5=-4$
For range $y=\ln (f(x))$ for $x>5$
or $x<1$ $f(x)>0$
Hence range of $g(x)$ is $R$.