Question

Consider the following function: f(x) = eˣ if x < 1, x³ if x ≥ 1. Given that a = 1, what is the value of f(a)?

1) e
2) 1
3) 1/e
4) 1/3

Answer 1

The value of f(a) when a = 1 is 1. Option 2

Step-by-step explanation:

The given function, f(x), has two defined expressions depending on the value of x. For x values less than 1, the function is represented as f(x) = eˣ, and for x values greater than or equal to 1, it is f(x) = x³. When a = 1, it falls into the category where x is greater than or equal to 1. Therefore, substituting a = 1 into the function, f(a) becomes f(1) = 1³, which simplifies to 1.

In this function, the transition occurs at x = 1, and since the value of a is given as 1, it precisely falls into the range where x is greater than or equal to 1. Substituting a = 1 into the function results in f(1) = 1³, which is equal to 1. Hence, when a = 1, the value of f(a) is 1.

Understanding the piecewise nature of functions is vital in accurately computing their values for specific inputs. In this case, the function has different definitions for distinct ranges of x, and evaluating f(a) requires identifying the appropriate expression based on the given value of a. Here, a = 1 falls into the region where x ≥ 1, so the expression x³ is used to find f(a), resulting in a value of 1.Option 2