Answer:
[tex]f^{-1}(x)=\dfrac{x-1}{2}[/tex]
Step-by-step explanation:
Given: f(x)=2x+1
To find: The inverse of f(x)
Step 1: Set f(x)=y
y = 2x + 1
Step 2: Switch x and y
x = 2y + 1
Step 3: Solve for y
2y=x-1
[tex]y=\dfrac{x-1}{2}[/tex]
We assumed y=f(x)
switch x and y
Thus, [tex]f^{-1}x=y[/tex]
Hence, The inverse of f(x)=2x+1 is [tex]f^{-1}(x)=\dfrac{x-1}{2}[/tex]
