Final answer:
The reciprocal of the function f(x) = -2x² / x⁷ is found by simplifying the function to f(x) = -2 / x⁵, so the correct answer is b. f⁻¹(x) = -2 / x⁵.
Step-by-step explanation:
The question asks for the reciprocal of the function f(x) = -2x² / x⁷. To find the reciprocal of a function, you simply take the inverse of the function. Starting with the given function, we can simplify it first by subtracting the exponents of x in the numerator and the denominator (as per the rules of exponents for division). This gives us f(x) = -2 / x⁵, because 2 - 7 equals -5. The negative exponent indicates that x to the fifth power is in the denominator. Therefore, the reciprocal of the function is b. f⁻¹(x) = -2 / x⁵.