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 = 0, X E R D. x + 5, x 6 R

Answer 1

The function is given as

`f(x)=(3)/(2-5x)`

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

`x=(3)/(2-5y)`

Now solve for y.

`2-5y=(3)/(x)`
`x=(3)/(2-5y)`
`2x-5xy=3`
`2x-3=5xy`
`y=(2x-3)/(5x)=(2)/(5)-(3)/(5)x`

Thus the inverse of the function is

`-(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\\e0,y\epsilon R\rbrace`