Answer:
The inverse of x² +1 is:
[tex]\sqrt{x-1},\:-\sqrt{x-1}[/tex]
Step-by-step explanation:
Given
y = x² + 1, x>0
We know that A function g is the inverse of a function f if for y = f(x), x = g(y)
y = x² +1
Replace x with y
x = y² + 1
solve for y
y² = x - 1
Taking square root
[tex]y=\:\sqrt{x-1},-\sqrt{x-1}[/tex]
Thus, the inverse of x² +1 is:
[tex]\sqrt{x-1},\:-\sqrt{x-1}[/tex]
