inal answer:
To evaluate (g-f)(2), substitute the value of 2 into the functions g(x) and f(x), and subtract the two values. g(2) = 2 and f(2) = -8/3. Therefore, (g-f)(2) = 14/3.
Step-by-step explanation:
To evaluate (g-f)(2), we need to substitute the value of 2 into the functions g(x) and f(x), and then subtract the two values.
First, let's evaluate g(x). The logarithm function log₄(x) gives us the exponent that 4 needs to be raised to in order to obtain x. So, g(2) is the exponent that 4 needs to be raised to in order to obtain 2. Since 4² = 16, we can say that g(2) = 2.
Next, let's evaluate f(x). Substituting x = 2 into the function (x³)/(x² - 2x - 3), we get f(2) = (2³)/(2² - 2(2) - 3) = 8/(4 - 4 - 3) = 8/(-3) = -8/3.
Finally, we subtract the value of f(2) from g(2): (g-f)(2) = g(2) - f(2) = 2 - (-8/3) = 2 + 8/3 = 6/3 + 8/3 = 14/3.