Answer:
[tex]f^{-1}(x) = \frac{x-5}{2}[/tex]
Step-by-step explanation:
[tex]f(x) = 2x+5[/tex]
Step 1) Replace y = f(x)
[tex]y = 2x+5[/tex]
Step 2) Exchange x and y
[tex]x =2y+5[/tex]
Step 3) Solve for y
[tex]x =2y+5[/tex]
Subtracting both sides by -5
[tex]x - 5= 2y[/tex]
[tex]2y = x-5[/tex]
Dividing both sides by 2
[tex]y = \frac{x-5}{2}[/tex]
Step 4) Replace [tex]y = f^{-1}(x)[/tex]
[tex]f^{-1}(x) = \frac{x-5}{2}[/tex]
