Question

Let g(x) = x² + x + 2, what is f(h + 1)?

A) f(I + h) = 12 + 2h + I
B) f(I + h) = 12 + 3h + 4
C) f(I + h) = 1
D) None of the above.

Answer 1

The correct evaluation of the function g(x) = x² + x + 2 for the input 'h + 1' is h² + 3h + 4, which corresponds to option B in the provided choices.

Step-by-step explanation:

The original question contains a typo. Assuming the function is g(x) = x² + x + 2 and we want to evaluate g(h + 1), we substitute 'h + 1' wherever we see 'x' in the function's formula:

g(h + 1) = (h + 1)² + (h + 1) + 2

g(h + 1) = h² + 2h + 1 + h + 1 + 2

g(h + 1) = h² + 3h + 4

Therefore, the correct answer is B) f(I + h) = 12 + 3h + 4, with the assumption that 'f' is the function in question and 'I' represents '1'. However, it is important to note that usually functions are denoted consistently and the original question seems to have a mismatch in notations (g and f), which could imply a transcription error. Nonetheless, the computed expression for the function applied to 'h+1' stands correct.