find inverse function of the following functions f(x)=3x+1

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You may use the following alternative method, hence, you may substitute y for f(x) such that:

`y = 3x + 1`

You need to solve for x the equation above, hence, you need to isolate the terms that contain x to one side, such that:

`y - 1 = 3x`

You need to divide the equation by 3 such that:

`(y - 1)/3 = x`

Hence, the equation above represents the equation of the inverse function `f^(-1)(y) = (y - 1)/3.`

Since the standard notation of a function uses x for variable, hence, you may write the function such that:

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

Hence, evaluating the inverse function yields `f^(-1)(x) = x/3 - 1/3.`

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lfryerda | High School Teacher | (Level 2) Educator

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If you have more than one question, you need to make separate posts.  

To find the inverse of a function, interchange x and y, and then solve for y.

`F(x)=3x+1`   interchange x and y

`x=3F^{-1}(x)+1`   solve for y

`x-1=3F^{-1}(x)`  divide by 3

`{x-1}/3=F^{-1}(x)`

The inverse function is `F^{-1}(x)={x-1}/3` .

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