Question

Consider the functions:

f(x) = 2
g(x) = 2x - 5
What is the value of (f.g)(3)?
A. 6
B. 8
C. 2
D. 11

Answer 1

To find the value of (f.g)(3), we compute g(3) = 2•(3) - 5 = 1, then apply f to this result, giving us f(g(3)) = f(1) = 2. The correct answer is 2, option C.

Step-by-step explanation:

The student asked for the value of (f.g)(3). This notation means we need to find the composition of the functions f and g at the point x = 3. Function f is given simply as f(x) = 2, which means for any input x, the output is always 2. Function g is defined by g(x) = 2x - 5. To find (f.g)(3), we first calculate g(3), and then apply the function f to that resultFirst, let's find g(3):
(3) = 2•(3) - 5 = 6 - 5 = 1.

Now, we apply function f to this result, which gives us:
f(g(3)) = f(1) = 2.

Therefore, the correct value of (f.g)(3) is 2, which corresponds to option C.