Determine whether the function ƒ(x) = x4 − 4x2 − 1 is even, odd or neither.?
回答 (5)
2016-05-30 8:42 pm
For an even function : f(x) = f(-x)
For an odd function : -f(x) = f(-x)
Now, f(x) = x⁴ - 4x² - 1
Then, f(-x) = (-x)⁴ - 4(-x)² - 1
f(-x) = x⁴ - 4x² - 1
Since f(x) = f(-x), then f(x) is an even function.
For an odd function : -f(x) = f(-x)
Now, f(x) = x⁴ - 4x² - 1
Then, f(-x) = (-x)⁴ - 4(-x)² - 1
f(-x) = x⁴ - 4x² - 1
Since f(x) = f(-x), then f(x) is an even function.
2016-05-30 8:38 pm
Well,
ƒ(x) = x^4 − 4x^2 − 1
therefore, for any real x
ƒ(-x) = (-x)^4 − 4(-x)^2 − 1
= x^4 - 4x^2 - 1
= ƒ(x)
therefore
function ƒ(x) is even <--- answer
hope it' ll help !!
ƒ(x) = x^4 − 4x^2 − 1
therefore, for any real x
ƒ(-x) = (-x)^4 − 4(-x)^2 − 1
= x^4 - 4x^2 - 1
= ƒ(x)
therefore
function ƒ(x) is even <--- answer
hope it' ll help !!
2016-05-30 8:39 pm
Since f(x) = f(-x) the function is even.
2016-05-30 8:38 pm
Does f(x) = f(-x)? If yes, then it's even.
Does it help to write it as f(x) = x^4 - 4x^2 - 1x^0? What do you notice about all the exponents?
Does it help to write it as f(x) = x^4 - 4x^2 - 1x^0? What do you notice about all the exponents?
2016-05-30 8:38 pm
x^4 would be an even function because the highest power is even
收錄日期: 2021-04-18 14:53:28
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