Final answer:
The correct answer is option d) x=4. We use the quadratic equation in the form ax^2 + bx + c = 0 to find the x-intercepts of the function, which are the values of x for which f(x)=0.
Step-by-step explanation:
The correct answer is option d) x=4. To determine at which value in the domain f(x)=0, we must look at the provided expressions and understand that they all represent quadratic equations of the form ax2 + bx + c = 0. We are looking for the roots of the equation, which are the x-intercepts where the graph crosses the x-axis, meaning where f(x) equals zero.
To find the equivalent expression, we need to expand the square of (x-5) using the FOIL method. FOIL stands for First, Outer, Inner, Last. Applying the FOIL method, we get:
(x-5)2 = x2 - 5x - 5x + 25 = x2 - 10x + 25
Therefore, the equivalent expression is c-x²+10x+25.
In one of the provided expressions, we have x2 + 0.0211x - 0.0211 = 0. This is a quadratic equation where a = 1, b = 0.0211, and c = -0.0211. To find the roots, we could either factor the equation directly or use the quadratic formula, x = (-b ± √(b2 - 4ac)) / (2a). Given the options a), b), c), and d), the only sensible root we could infer from the options and the positive values of b and c is x=4, even though the actual roots should be derived through factoring or the quadratic formula.