Answer:
[tex]f^{-1}(x)=2\pm\sqrt{x-3}[/tex]
Step-by-step explanation:
we have
[tex]y=(x-2)^2+3[/tex]
step 1
Exchange the variables (x for y and y for x)
so
[tex]x=(y-2)^2+3[/tex]
Isolate the variable y
step 2
[tex]x=(y-2)^2+3[/tex]
subtract 3 both sides
[tex](y-2)^2=x-3[/tex]
step 3
square root both sides
[tex]y-2=\pm\sqrt{x-3}[/tex]
step 4
Adds 2 both sides
[tex]y=2\pm\sqrt{x-3}[/tex]
step 5
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=2\pm\sqrt{x-3}[/tex]
