let f be the function defined above. for what value of c, if any, is f continuous at x = 3? a 2 b 4 c 6 d…

Explanation:

Step1: Recall continuity condition

For a function to be continuous at $x = a$, $\lim_{x\rightarrow a^{-}}f(x)=\lim_{x\rightarrow a^{+}}f(x)=f(a)$. Here we assume the left - hand limit behavior is different from the right - hand limit behavior for $x = 3$. Let's assume the left - hand side function is not given, but for the right - hand limit as $x\rightarrow3^{+}$, we consider $y = 2c+\frac{3}{x - 2}$.

Step2: Calculate the right - hand limit

We find $\lim_{x\rightarrow3^{+}}(2c+\frac{3}{x - 2})$. Substitute $x = 3$ into the expression $2c+\frac{3}{x - 2}$. We get $2c+\frac{3}{3 - 2}=2c + 3$. For the function to be continuous, this value must be well - defined and match the left - hand limit (if the function is defined on the left of $x = 3$). But since we have no information about the left - hand side and no way to equate this value to a known left - hand limit value, and also no other conditions are given to solve for $c$ in terms of a known left - hand behavior, we conclude there is no such $c$ that can make the function continuous just from the given right - hand side expression and the lack of left - hand side information.

Answer:

D. There is no such $c$.