Question

$f(x) = \frac{m}{x - 1} + n$, x≠k

given, f(2)=3 and f(3)=2

find the value of k​

Answer 1

Answer:

Step-by-step explanation:

$f(2)=\frac{m}{2-1}+n\\\\f(2)=\frac{m}{1}+n\\\\f(2)=m+n\\\\m+n=3\\m=3-n------(i)\\\\f(3)=\frac{m}{3-1}+n\\\\f(3)=\frac{m}{2}+n\\\\f(3)=\frac{m}{2}+\frac{n*2}{1*2}\\\\f(3)=\frac{m}{2}+\frac{2n}{2}\\\\f(3)=\frac{m+2n}{2}\\\\f(3)=2\\\\\frac{m+2n}{2}=2\\\\m+2n=2*2\\\\m+2n=4---------(ii)\\\\3-n+2n=4------{using(i)}\\\\3+n=4\\\\n=4-3\\\\n=1\\\\m=3-n=3-1\\\\m=2$