Answer:
Step-by-step explanation:
[tex]\text{If}\ f(-x)=f(x)\ \text{then}\ f(x)\ \text{is an even function.}\\\\\text{If}\ f(-x)=-f(x)\ \text{then}\ f(x)\ \text{is an odd function.}[/tex]
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[tex]f(x)=-3x^4+7x^2\\\\f(-x)=-3(-x)^4+7(-x)^2=-3x^4+7x^2\\\\f(-x)=f(x)[/tex]
The function f(x) = -3x⁴ + 7x² is an even function because f(-x) = f(x) = -3x⁴ + 7x²
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = -3x⁴ + 7x²
To check whether the function is odd or even, plug x → -x in the function:
f(-x) = -3(-x)⁴ + 7(-x)²
f(-x ) = -3x⁴ + 7x²
f(-x) = f(x)
The function is even.
Thus, the function f(x) = -3x⁴ + 7x² is an even function because f(-x) = f(x) = -3x⁴ + 7x²
Learn more about the function here:
brainly.com/question/5245372
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