Question

The function $y=\frac{2x-1}{x-2}(x\ne 2)$ -

• A. Has its own inverse
• B. Decreases for all values of x
• C. Has a graph entirely above x - axis
• D. Is bound for all x

Answer 1

Answer: (A), (B)

Has its own inverse
Decreases for all values of x

$y=\frac{2x-1}{x-2}$
$xy-2y=2x-1$
$xy-2x=2y-1$
$x=\frac{2y-1}{y-2}$
Inverse of the function exists
$y=\frac{2(x-2)+3}{x-2}$
$y=2+\frac{3}{x-2}$
$\frac{dy}{dx}=\frac{-3}{(x-2{)}^2}<0$
$\therefore$ y decreases $\forall xϵR$