If graph of the function y=f(x) is continuous and passes through point (3,1) then displaystyle lim x arrow 3 ( log e(3 f(x)-2)/2(1-f(x))) is equal

Question

If graph of the function y=f(x) is continuous and passes through point (3,1) then displaystyle lim x arrow 3 ( log e(3 f(x)-2)/2(1-f(x))) is equal (A) (3/2) (B) (1/2) (C) -(3/2) (D) -(1/2)

Tardigrade Admin · Accepted Answer

Since y=f(x) is passing through the point (3,1), f(3)=1. Also, y=f(x) is continuous. ∴ displaystyle lim x arrow 3 f(x)=1 ∴ displaystyle lim x arrow 3 ( log e (3 f(x)-2)/2(1-f(x))) = displaystyle lim x arrow 3 ( log e (1+3(f(x)-1))/-2(f(x)-1)) =-(3/2)

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

$\frac{3}{2}$

$\frac{1}{2}$

$- \frac{3}{2}$

$- \frac{1}{2}$

Since $y = f (x)$ is passing through the point $(3, 1), f (3) = 1$ .
Also, $y = f (x)$ is continuous.
$∴ x \to 3 lim f (x) = 1$
$∴ x \to 3 lim \frac{lo g _{e} ( 3 f ( x ) - 2 )}{2 ( 1 - f ( x ))}$
$= x \to 3 lim \frac{lo g _{e} ( 1 + 3 ( f ( x ) - 1 ))}{- 2 ( f ( x ) - 1 )}$
$= - \frac{3}{2}$

Q. If graph of the function y=f(x) is continuous and passes through point (3,1) then x→3lim​2(1−f(x))loge​(3f(x)−2)​ is equal

23​

21​

−23​

−21​