If graph of the function `y=f(x)` is continuous and passes through point (3, 1) then `lim_(xrarr3) (log_(e)(3f(x)-2))/(2(1-f(x)))` is equal

Options

A. `(3)/(2)`
B. `(1)/(2)`
C. `-(3)/(2)`
D. `-(1)/(2)`

Answer

C

Explanation

Since y = f(x)is passing through the point (3, 1), f(3) = 1.
Also, `y=f(x)` is continuous.
`therefore" "underset(xrarr3)(lim)f(x)=1`
`therefore" "underset(xrarr3)(lim)(log_e(3f(x)-2))/(2(1-f(x)))`
`" "=underset(xrarr3)(lim)(log_(e)(1+3(f(x)-1)))/(-2(f(x)-1))`
`" "=-(3)/(2)`