Question

The function f is defined as $f=\left\{\right(x,y)|y=\frac{2x+1}{x-3}$ where $x\ne 3\}$. Find the value of K so that the inverse of f will be $f^{-1}=\left\{\right(x,y)|y=\frac{3x+1}{x-k}$ where $x\ne K\}$

• A. 1
• B. 2
• C. 3
• D. 4
• E. 5

Answer 1

The correct option is B 2

• Given $f\left(x\right)=\frac{2x+1}{x-3}$ , let it be $y$ , we get $y=\frac{2x+1}{x-3}$
• Which implies $xy-3y=2x+1$ , which gives $x=\frac{3y+1}{y-2}=f^{-1}\left(y\right)$
• Therefore the value of $k$ is $2$