Question

Whats the inverse of the function of y=3x+1

Answer 1

Given: A function

`f(x)=3x+1`

Required: To find the inverse of the given function.

Explanation: We will use the concept of inverse functions to find out the inverse of f(x). Let

`\begin{gathered} f(x)=y \\ y=3x+1 \end{gathered}`

Interchange x and y,

`x=3y+1`

Now express y in terms of x as follows

`y=(x-1)/(3)`

From the definition of an inverse function,

`f(x)=y\Rightarrow x=f^(-1)(y)`

Therefore,

`f^(-1)(y)=(x-1)/(3)`

Thus the inverse of y=3x+1 is

`f^(-1)(x)=(x-1)/(3)`

Final Answer:

`f^(-1)(x)=(x-1)/(3)`