Your Answer is

Correct Answer is K

Explanation

For f(x), there are three domains. In the first domain x ∈ (- ∞ , 1 ), the image of y = x² - 2 is a parabola with an upward opening.

In the second domain x ∈ n (1,5), y = x - 7 is a straight line with a slope of 1, and y = -5 when x = 2.

In the third domain x ∈ [5, ∞ ), y = -x +4 is a straight line with a slope of -1.

According to the function image, the opening of the parabola can exclude the answers F and G, and according to the non-repetitive domain of the function, H and J can be excluded, then the correct answer is K