Math

QuestionFind the inverse of the function R(x)=2x+1R(x)=2x+1, which is R1(x)=x12R^{-1}(x)=\frac{x-1}{2}.

Studdy Solution

STEP 1

Assumptions1. The function is R(x)=x+1R(x)=x+1 . We are asked to find the inverse of this function, denoted as R1(x)R^{-1}(x)

STEP 2

To find the inverse of a function, we first replace the function notation R(x)R(x) with yy. This gives usy=2x+1y =2x +1

STEP 3

Next, we swap xx and yy. This gives usx=2y+1x =2y +1

STEP 4

Now, we solve this equation for yy to get the inverse function. First, subtract1 from both sidesx1=2yx -1 =2y

STEP 5

Then, divide both sides by2R1(x)=x12R^{-1}(x) = \frac{x -1}{2}So, the inverse of the function R(x)=2x+1R(x)=2x+1 is R1(x)=x12R^{-1}(x)=\frac{x-1}{2}.

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