Question

Let (x) = 2x^3 − 9x^2 / (13x − 6), and (x) = x − 2. Find:

a) f(0)

b) g(3)

c) f(g(2))

d) g(f(1))

Answer 1

The computation of f(0), f(g(2)), and g(f(1)) cannot be completed without the actual function f(x). However, g(3) can be calculated and is equal to 1.

Step-by-step explanation:

The student is asking to evaluate functions for certain values. Let's denote the first function as f(x) and the second one as g(x).

• a) f(0): To find f(0), we substitute x with 0 in the first given function. Unfortunately, the function of f(x) is not provided in the question, so we cannot calculate this.
• b) g(3): To find g(3), we substitute x with 3 into g(x), resulting in g(3) = 3 - 2 = 1.
• c) f(g(2)): First, we evaluate g(2) which gives us 2 - 2 = 0. Then, we would substitute this result into f(x), but since f(x) is not provided, we cannot finish this computation.
• d) g(f(1)): First, we would need to find f(1), but without the actual function f(x), this can't be computed. Afterward, the result would be substituted into g(x), which is also not possible in this case.

As the functions f(x) and g(x) were not fully provided, we cannot complete calculations for parts a), c), and d) of the question.