Question

Find the inverse of f(x) =3/x -10

Answer 1

`f^(-1)(x)\text{ = }(3)/(x+10)`

Step-by-step explanation:

f(x) = 3/x -10

To get the inverse, let's make f(x) = y

y = 3/x -10

interchange y and x:

x = 3/y - 10

make y the subject of formula:

`\begin{gathered} x\text{ =3/y - 10/1} \\ x\text{ = }\frac{3\text{ - 10y}}{y} \\ \text{cross multiply: } \\ xy\text{ = }3\text{ - 10y} \end{gathered}`
`\begin{gathered} xy\text{ + 10y = 3} \\ y(x\text{ + 10) = 3} \\ y\text{ = }(3)/(x+10) \\ f^(-1)(x)\text{ = }(3)/(x+10) \end{gathered}`