Final answer:
To find the square root of f(x) using the bisection method, we identify an interval where f(x) changes sign. Based on the given options, we check the non-negative values and find [C. 1.5, D. 2] as a suitable interval. After confirming a change in sign within this interval, we would apply the bisection method.
Step-by-step explanation:
The question is asking to find the square root of the function f(x) = x√x + 1 using the bisection method. Before applying the bisection method, we need to identify an interval [a, b] where the function changes sign, indicating that there is a root within that interval.
From the options provided, we see that the values of x are negative and positive. A function involving square roots can have real values for the root only when the radicand is non-negative. Hence, for x√x to be real and non-negative, x must be non-negative itself. Looking at the options, the only suitable interval that starts with a non-negative value is [C. 1.5, D. 2].
To confirm this interval, we would calculate f(1.5) and f(2), expecting a sign change. After identifying the correct interval, we would then apply the bisection method, which involves iteratively bisecting the interval and selecting the subinterval that contains the root, based on a change in sign of f(x) values at the endpoints, until sufficient accuracy is achieved.