Inverse and radical functions precalculus

Question

Let f(x)=(x+5)^2 Find a domain on which f is one to one and non decreasing. Find the inverse of f restricted to this domain f^-1(x)=

Answer 1

a. Domain of f that is one to one and non decreasing:

Since (x+5)² is quadratic U-shaped graph with vertex at (-5,0). The non decreasing part is from (-5, infinity), and that is also the 0ne-to-one.

b. Inverse

interchange x and y or f(x) in the equation:

x = (y+5)²

Solve for y:

x^0.5 = y + 5

y = x^0.5 - 5 ,

this means f^-1(x) = sqrt(x) - 5, and this is only good for the domain given above.