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Home > CALC > Chapter 2 > Lesson 2.3.3 > Problem 2-125

2-125.
  1. Determine if the following functions are even, odd, or neither. Explain how you determined your choice. Homework Help ✎

    1. y = sin2 x

y = sin2x = (sinx)(sinx)

y = sinx is an odd function. Definition of odd functions: f(−x) = −f(x) Therefore, sin(−x) = −sin(x).

Explore what y = sin2(−x) looks like:
y = sin2(−x)
= (sin(−x))(sin(−x))
=(−sinx)(−sinx)
= sin2x

Hence sin2(−x) = sin2(x).
This is the definition of an even function: f(−x) = f(x).

Test for even: f(a) = f(−a)

f(a) ≠ f(−a); not even

Test for odd: f(−a) = −f(a)...