Answer:
yes, no, no
Step-by-step explanation:
For odd functions : −f(x) = f(−x) for all x
For even functions :f(x) = f(−x) for all x
1) -f(x)= -2x^3 -2x
f(-x) = -2x^3-2x
yes
2 ) f(-x) = 5x^3 -4 ≠ f(x)
no
3 ) f(-x) = -4x -4 ≠ f(x)
no
1) [tex]f(-x) = -2x^3-2x[/tex]
The function [tex]f(x)=2x^3 + 2x[/tex] is odd function.
2 ) [tex]f(-x) = 5x^3 -4[/tex] ≠ f(x)
The function [tex]f(x) = -5x^3 - 4[/tex] is not even function.
3 ) f(-x) = -4x - 4 ≠ f(x)
The function f(x) = 4x - 4 is not an even even function.
If we obtain an expression that exists equivalent to f(x), we have an even function; if we obtain an expression that stands equivalent to -f(x), we contain an odd function; and if neither occurs, it is neither!
For odd functions :
−f(x) = f(−x) for all x
For even functions :
f(x) = f(−x) for all x
1) [tex]f(-x) = -2x^3-2x[/tex]
Therefore, the function [tex]f(x)=2x^3 + 2x[/tex] is odd function.
2 ) [tex]f(-x) = 5x^3 -4[/tex] ≠ f(x)
Therefore, the function [tex]f(x) = -5x^3 - 4[/tex] is not even function.
3 ) f(-x) = -4x - 4 ≠ f(x)
Therefore, the function f(x) = 4x - 4 is not an even even function.
To learn more about an odd function and an even function
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