Given the function f(x) = 4x - 1.

Here's the solution to the problem: Given the function f(x) = 4x - 1. a) Find the value of f(2.999) and f(3.001). Step 1: Calculate f(2.999). Substitute x = 2.999 into the function: f(2.999) = 4(2.999) - 1 f(2.999) = 11.996 - 1 f(2.999) = 10.996 Step 2: Calculate f(3.001). Substitute x = 3.001 into the function: f(3.001) = 4(3.001) - 1 f(3.001) = 12.004 - 1 f(3.001) = 11.004 The values are f(2.999) = 10.996 and f(3.001) = 11.004. b) Is function f(x) continuous at the point x=3? Give reason. Yes, the function f(x) = 4x - 1 is continuous at the point x=3. Reason: A function f(x) is continuous at a point x=c if three conditions are met: 1. f(c) is defined. 2. _x c f(x) exists. 3. _x c f(x) = f(c). For f(x) = 4x - 1 at x=3: 1. f(3) = 4(3) - 1 = 12 - 1 = 11. So, f(3) is defined. 2. _x 3 (4x - 1) = 4(3) - 1 = 11. So, the limit exists. 3. _x 3 f(x) = 11 and f(3) = 11. Thus, _x 3 f(x) = f(3). Alternatively, and more concisely, f(x) = 4x - 1 is a polynomial function. All polynomial functions are continuous for all real numbers. Therefore, f(x) is continuous at x=3.