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.