Question

What is the appropriate expanded version of f(x)?

a) f(x) = x² + 2x + 1
b) f(x) = (x + 1)²
c) f(x) = x² - 2x + 1
d) f(x) = (x - 1)²

Answer 1

The expanded version of the function f(x) = (x + 1)² is f(x) = x² + 2x + 1, and for f(x) = (x - 1)², it is f(x) = x² - 2x + 1. We match these to the options given, identifying the corresponding correct answer as option a or c respectively.

Step-by-step explanation:

The student appears to be asking which expanded form of a function f(x) corresponds to one of the provided options. Assuming the student is asking for the expanded form of f(x) = (x + 1)² or f(x) = (x - 1)², the correct expanded version would be obtained by squaring the binomial.

Expanding the binomial f(x) = (x + 1)² gives f(x) = x² + 2x + 1, and expanding f(x) = (x - 1)² gives f(x) = x² - 2x + 1.

Comparing with the given options, we can identify the correct expanded form:

• If f(x) = (x + 1)², then the expanded form is f(x) = x² + 2x + 1, which corresponds to option a.
• If f(x) = (x - 1)², then the expanded form is f(x) = x² - 2x + 1, which corresponds to option c.