Final answer:
The real zero of the function y = (x-12)^3 - 7 is found by setting y to zero and solving for x, which results in the answer x = 12 + 7^(1/3).
Step-by-step explanation:
The given function is y = (x-12)^3 - 7. To find the real zeroes of the function, we need to set y equal to zero. So, the equation becomes 0 = (x-12)^3 - 7. Solving for x, we add 7 to both sides, obtaining (x-12)^3 = 7. Taking the cube root of both sides gives us x-12 = 7^(1/3). Adding 12 to both sides, we find that the only real zero of the function is x = 12 + 7^(1/3).
Therefore, the answer is c. x = 12 + 7^(1/3), which is the real zero of the function.