Answer:
[tex]y=\frac{x-3}{2}[/tex]
Step-by-step explanation:
The given function is
[tex]f(x)=2x+3[/tex]
To find the inverse of this function, we have to replace [tex]f(x)[/tex] for [tex]y[/tex], and then isolate [tex]x[/tex], as follows
[tex]y=2x+3\\y-3=2x\\2x=y-3\\x=\frac{y-3}{2}[/tex]
Then, we have to switch variables, as follows
[tex]y=\frac{x-3}{2}[/tex]
Therefore, the inverse of the given function is
[tex]y=\frac{x-3}{2}[/tex]
The graph attached shows both functions. The blue line is the inverse of [tex]f(x)[/tex]
