1)If f(x) = logx, then what is the value of f^-1 (0)?
2)Determine whether each of the following functions is even or odd.
y=1-x^3 &
y=5^x
3)Let y = f(x) be a function such that for any real numbers a and b, f(a+b)+f(a-b) = 2[f(a)+f(b)]. Prove that f(x) is an even function.
Special Function
2010-07-30 5:27 am
回答 (1)
2010-07-30 6:54 am
✔ 最佳答案
1.f(x) = log x
Let y= log x
x = 10^y
f^-1(x) = 10^x
f^-1(0) = 10^0 =1
2.let f(x) = y
For y = 1-x^3
f(-x) = 1-(-x)^3 = 1+x^3 ≠ f(x) ≠ -f(x)
For y=5^x
f(-x) = 5^(-x) = 1/5^x ≠ f(x) ≠ -f(x)
So, both of them are neither odd or even.
3.
Set a=b=0, we get f(0)=0
f(0+x)+f(0-x)=2[f(0)+f(x)]
f(x)+f(-x) = 2f(x)
f(-x)=f(x)
f is an even function.
收錄日期: 2021-04-23 21:30:42
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100729000051KK01846