Final answer:
After calculating g(5) as 4.75, we find f(g(5)) to be 11.3125, which does not match any of the provided options, suggesting possibly incorrect options or a calculation mistake.
Step-by-step explanation:
To find the value of f(g(x)) when f(x) = x² - 3x + 3 and g(x) = x - 1/4, and with x = 5, we first evaluate g(5) and then use that value to find f(g(5)).
First, we find g(5):
g(5) = 5 - 1/4
= 4.75
Next, we compute f(g(5)) which is f(4.75):
f(4.75) = (4.75)² - 3(4.75) + 3
= 22.5625 - 14.25 + 3
= 11.3125
None of the options (A) -3, (B) 1, (C) 7, (D) 13 match the result, therefore there may be an error with the provided options or a mistake was made in the calculation.