Final answer:
To determine h(x - 1) for the given function h(x), substitute (x-1) in place of x and simplify the expression.
Step-by-step explanation:
To determine h(x - 1) for the function h(x) = [4x /(x² - 5x + 4)], we need to substitute (x - 1) in place of x in the function. This means replacing x with (x - 1) wherever it appears in h(x). So, h(x - 1) = [4(x - 1) / ((x - 1)² - 5(x - 1) + 4)].
Next, we simplify the expression inside the square brackets. Expanding the numerator, we have 4x - 4, and expanding the denominator, we have (x - 1)² - 5(x - 1) + 4 = x² - 2x + 1 - 5x + 5 + 4 = x² - 7x + 10.
Therefore, h(x - 1) = [4(x - 1) / (x² - 7x + 10)].