Answer:
1. Start with the original function g(x) = x^2 - 10x.
2. Replace g(x) with y to express the function as an equation: y = x^2 - 10x.
3. Swap the x and y variables to switch the roles of the dependent and independent variables: x = y^2 - 10y.
4. Rearrange the equation to isolate y: y^2 - 10y - x = 0.
5. This equation is a quadratic equation in terms of y. To solve it, we can use the quadratic formula: y = (-b ± √(b^2 - 4ac))/(2a), where a = 1, b = -10, and c = -x.
6. Plug in the value of x = 11 into the quadratic formula: y = (-(-10) ± √((-10)^2 - 4(1)(-11)))/(2(1)).
7. Simplify the expression: y = (10 ± √(100 + 44))/2.
8. Further simplify the expression: y = (10 ± √(144))/2.
9. Simplify the square root: y = (10 ± 12)/2.
10. Split the equation into two cases:
a) y = (10 + 12)/2 = 22/2 = 11.
b) y = (10 - 12)/2 = -2/2 = -1.
11. Since we are given x ≥ -5, the only valid solution is y = 11. Therefore, g^(-1)(11) = 11.
In summary, g^(-1)(11) = 11 when considering the given restriction x ≥ -5.
Explanation: