Answer:
[tex]f^{-1}(x)=\frac{x}{2}-\frac{1}{2}[/tex]
Step-by-step explanation:
It is called an inverse or reciprocal function of [tex]f[/tex] to another function [tex]f^{-1}[/tex] that fulfills that:
If [tex]f(a)=b[/tex], then [tex]f^{-1} (b)=a[/tex]
To calculate the inverse of the function [tex]y=2x+1[/tex]
[tex]f(x)=y[/tex]
So, rewritting the function
[tex]f(x)=2x+1[/tex]
Changing the x for y
[tex]x=2y+1[/tex]
Let's clear y
[tex]y=\frac{x-1}{2}[/tex]
Ordering the function above
[tex]y=\frac{x}{2}-\frac{1}{2}[/tex]
So, the inverse of the function [tex]f(x)=2x+1[/tex] is:
[tex]f^{-1}(x)=\frac{x}{2}-\frac{1}{2}[/tex]
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