F(x) = (m)/(x - 1) + n, x≠k given, f(2)=3 and f(3)=2 find the value of k​

Question

`f(x) = (m)/(x - 1) + n`, x≠k

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

find the value of k​

Answer 1

Explanation:

`f(2)=(m)/(2-1)+n\\\\f(2)=(m)/(1)+n\\\\f(2)=m+n\\\\m+n=3\\m=3-n------(i)\\\\f(3)=(m)/(3-1)+n\\\\f(3)=(m)/(2)+n\\\\f(3)=(m)/(2)+(n*2)/(1*2)\\\\f(3)=(m)/(2)+(2n)/(2)\\\\f(3)=(m+2n)/(2)\\\\f(3)=2\\\\(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`