Question

3 = 2-5x State The function f is given by f(x): the domain of f-1. A. {yly = 5, y E R} B. {yly = 0, y E R} C. {x|x = 0, X E R} D. {x|x + 5, x 6 R}

Answer 1

The function is given as

$f(x)=\frac{3}{2-5x}$

To find the inverse of the function, replace x with y.

$x=\frac{3}{2-5y}$

Now solve for y.

$2-5y=\frac{3}{x}$$x=\frac{3}{2-5y}$$2x-5xy=3$$2x-3=5xy$$y=\frac{2x-3}{5x}=\frac{2}{5}-\frac{3}{5}x$

Thus the inverse of the function is

$-\frac{3-2x}{5x}$

Now to find the domain of the function is

The domain of the function is the set of values of x for which the function is defined.

The domain of the inverse function is

$(-\infty,0)\cup(0,\infty)$

Hence the correct option is B.

$\lbrace y|y\ne0,y\epsilon R\rbrace$