Question

If graph of the function $y=f(x)$ is continuous and passes through point $(3,1)$ then $\displaystyle\lim _{x \rightarrow 3} \frac{\log _{e}(3 f(x)-2)}{2(1-f(x))}$ is equal

• A. $\frac{3}{2}$
• B. $\frac{1}{2}$
• C. $-\frac{3}{2}$
• D. $-\frac{1}{2}$

Answer 1

Answer: (C)

Since $y=f(x)$ is passing through the point $(3,1), f(3)=1$.
Also, $y=f(x)$ is continuous.
$\therefore \displaystyle\lim _{x \rightarrow 3} f(x)=1$
$\therefore \displaystyle\lim _{x \rightarrow 3} \frac{\log _{ e }(3 f(x)-2)}{2(1-f(x))} $
$= \displaystyle\lim _{x \rightarrow 3} \frac{\log _{ e }(1+3(f(x)-1))}{-2(f(x)-1)} $
$=-\frac{3}{2}$