Answer: Since the square root of a negative number is not a real number, there are no real solutions to this equation, and therefore no values of x for which f(x) = g(x).
Explanation:
To find all values of x for which f(x) = g(x), we can set the two functions equal to each other and solve for x:
-x² + 5 = -2x + 2
Expanding the right-hand side:
-x² + 5 = -2x + 2
-x² + 2x + 3 = 0
Solving for x using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 2, and c = 3
x = (-2 ± √(2² - 4(1)(3))) / 2(1)
x = (-2 ± √(4 - 12)) / 2
x = (-2 ± √(-8)) / 2
Since the square root of a negative number is not a real number, there are no real solutions to this equation, and therefore no values of x for which f(x) = g(x).