A formula for a function y=f (x) is f (x) = x^2-10x, xless than or equal 5. Find f^-1 (x) and indentify the domain and range of f^-1 (x). Is f (f^-1 (x))) = f^-1 (f (x)) = x?

F (x) = x² - 10x, f⁻¹ (x) = ?

1st find the missing square of x²-10x, = = > (x-5) ² - 25

y = (x-5) ² - 25; replace x by y and v0ce versa: x = (y-5) ² - 25

or

(y-5) ² = x+25

y-5 = √ (x+25) and y = √ (x+25) - 5

Domain = {x∈R: X> = 25} AND Range = {y∈R: y> = 5}