Question

For the following, find f(2.1) and f(4).

Answer 1

(a) f(2.1) = 2.205 and f(4) = 2

Explanation:

You want to evaluate a piecewise-defined function to find f(2.1) and f(4).

Domain

The first step in evaluating a piecewise defined function is to match the argument value with the appropriate domain.

• for f(2.1), you want to use the definition for the domain 2 < x < 4
• for f(4), you want to use the definition for the domain 4 ≤ x < 8

Function evaluation

Once you have identified the function you are evaluating, substitute the argument for the variable and carry out the arithmetic in the usual way.

• f(2.1) = 1/2(2.1)² = 1/2(4.41) = 2.205
• f(4) = log₂(4) = log₂(2²) = 2

The desired function values are f(2.1) = 2.205 and f(4) = 2.

Answer 2

A

Explanation:

Comment

The tricky part is f(4)

Log part

That is defined by log_2 which means that the base used for the log is 2.

We don't have log_2 on our calculators so you have to create it.

Substitute 4 for x

log_2 (4) = log_10(4)/ log_10 (2) Which your calculator can handle

log_2 (4) = Log(4)/ log(2) = 2

f(x) = 1/2 x^2

x = 2.1

Only answers a and b are correct, but which one is right? 2.1 is between 2 and 4. So you choose f(x) = 1/2 x^2

1/2 2.1^2 = 1/2 4.41 = 2.205

Answer

A