Using inverse function concepts, it is found that:
- The inverse of the function is [tex]y = \sqrt{x + 3} - 1[/tex], and the domain of the inverse function is [tex][-3, \infty][/tex].
- A function will have an inverse if for each output, there is only one respective input.
- The domain of the inverse is the range of the original function.
The function given is:
[tex]f(x) = (x + 1)^2 - 3[/tex]
- It's range is [tex][-3, \infty][/tex], which will be the domain of the inverse.
To find the inverse, we exchange x and y, and isolate y, then:
[tex]y = (x + 1)^2 - 3[/tex]
[tex]x = (y + 1)^2 - 3[/tex]
[tex](y + 1)^2 = x + 3[/tex]
[tex]\sqrt{(y + 1)^2} = \sqrt{x + 3}[/tex]
[tex]y + 1 = \sqrt{x + 3}[/tex]
[tex]y = \sqrt{x + 3} - 1[/tex]
The inverse of the function is [tex]y = \sqrt{x + 3} - 1[/tex], and the domain of the inverse function is [tex][-3, \infty][/tex].
A similar problem is given at https://brainly.com/question/13160937
