Question

Find the inverse of the linear function y= 1/2x+3

Answer 1

Answer: The inverse of the given function is
`y=2x-6.`

Step-by-step explanation: We are given to find the inverse of the following linear function :

`y=(1)/(2)x+3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`(i)`

The inverse of y = f(x) is written as

`x=f^(-1)(y).`

Substituting the above in equation (i), we get

`y=(1)/(2)x+3\\\\\Rightarrow y=(1)/(2)f^(-1)(y)+3\\\\\Rightarrow (1)/(2)f^(-1)(y)=y-3\\\\\Rightarrow f^(-1)(y)=2(y-3)\\\\\Rightarrow f^(-1)(y)=2y-6.`

Thus, the inverse of the given function is
`y=2x-6.`