Question

If $f\left(x\right)=(1-x{)}^{1/2}$ and $g\left(x\right)=\ln \left(x\right)$ then the domain of $\left(gof\right)\left(x\right)$ is

• A. $(-\infty ,2)$
• B. $(-1,1)$
• C. $(-\infty ,1]$
• D. $(-\infty ,1)$

Answer 1

Answer: (D)

$(-\infty ,1)$

Given $f\left(x\right)=(1-x{)}^{\frac{1}{2}}$ and $g\left(x\right)=ln\left(x\right)$

$gof\left(x\right)$

$=g\left(f\right(x\left)\right)$
$=\ln {(1-x)}^{1/2}$
$=\frac{1}{2}\ln (1-x)$
$\therefore$ For the composite function to be defined $1-x>0$
$x<1$
$\therefore$ Domain is $(-\infty ,1)$