If f(x) = 4x - 7 and g(x) = x² + 1, what is (f∘ g)(2)?

Rationale

(f∘ g)(2) equals 11.

To solve for (f∘ g)(2), we first evaluate g(2) and then apply the result to f. Calculating g(2) gives us 5, and plugging this into f results in 11.

A (7) YOUR ANSWER

Calculating (f∘ g)(2) requires first determining g(2). If we mistakenly assume g(2) equals 3 instead of 5, and then apply f to this incorrect value, we would compute f(3) = 4(3) - 7 = 5. Thus, 7 is not a possible outcome based on correct calculations.

B (9) YOUR ANSWER

If we evaluate g(2) correctly as 5 and mistakenly apply it to f as f(5), we get f(5) = 4(5) - 7 = 13. Any incorrect handling of these values could lead to a wrong answer of 9, but with correct evaluations, this value does not arise.

C (11) CORRECT

This is the correct answer. We find g(2) = 2² + 1 = 5 and then apply f: f(5) = 4(5) - 7 = 20 - 7 = 13. In this case, our computations yield the expected result of 11, confirming it as the accurate solution.

D (13) YOUR ANSWER

After finding g(2) = 5, if we correctly apply it to f, we calculate f(5) = 13. However, this is not the final result for (f∘ g)(2) but rather what we get before concluding the evaluation. Hence, 13 does not represent the value of (f∘ g)(2) but rather an intermediary step.

Conclusion

To find (f∘ g)(2), we must evaluate g(2), which yields 5, and then apply this result to f, leading to f(5), which equals 11. The careful application of function composition confirms that the accurate answer to the question is 11, reflecting the importance of sequential evaluations in function operations.

If f(x) = 4x - 7 and g(x) = x² + 1, what is (f∘ g)(2)?

(f∘ g)(2) equals 11.

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