Question

Given f(x) = 2x - 1 and h(x) = 3, find (f ◦ h)(1).

Which of the following is the value of (f ◦ h)(1)?

a) 4
b) 5
c) 6
d) 7

Answer 1

To find (f ◦ h)(1), we first find h(1), which is always 3, and then we substitute that into f(x) = 2x - 1. Calculating f(3) gives us 6 - 1, which results in a value of 5. Hence, the correct answer is option (b) 5.

Step-by-step explanation:

The student is asked to find (f ◦ h)(1), which means that we need to first apply the function h to 1 and then apply the function f to the result of h(1). Since h(x) = 3, irrespective of the input, h(1) = 3. Next, we apply the f function: f(h(1)) = f(3). The function f is defined as f(x) = 2x - 1, so we substitute x with 3: f(3) = 2 × 3 - 1 = 6 - 1 = 5.

Therefore, the value of (f ◦ h)(1) is 5, which corresponds to option (b).