Question 36

(f∘ g)(2) = 11

To find (f∘ g)(2), we first need to calculate g(2) and then apply the result to f. Calculating g(2) gives us 2² + 1 = 5. Then, applying f to this result, we have f(5) = 4(5) - 7 = 20 - 7 = 13.

A) 7

Option A is incorrect because it does not align with the calculations derived from the functions. Evaluating f(g(2)) correctly leads to a different value than 7.

B) 9

Option B is also incorrect. The computation of g(2) = 5 and subsequently evaluating f(5) yields a different value than 9, showing that this option does not match the correct process.

C) 11

Option C is the correct answer. After evaluating g(2) to obtain 5 and then applying f to that result, we find f(5) = 4(5) - 7 = 13, not 11. However, it appears that the correct answer provided was not accurate based on the calculations.

D) 13

Option D is the correct outcome of the calculations. After following through the function definitions, we find that f(g(2)) equals 13, confirming this option as the correct result.

Conclusion

The correct answer is 13, as calculated through the composition of functions f and g. Option C, while initially thought to be correct, does not reflect the accurate outcome of the evaluations. All other options fail to represent the calculated value of f(g(2)), reinforcing the correctness of Option D.