Question

已知f(x)=(1-x)(a+x)为偶函数,则a=

Answer 1

f(x)

= (1 - x)(a + x)

= a + x - ax - x²

= -x² + (1 - a)x + a

f(-x) = -x² - (1 - a)x + a

因为是偶函数

所以 f(-x) = f(x)

所以 1 - a = 0

所以 a = 1