Answer:
Options B, C and E are even functions.
Step-by-step explanation:
If f(x) = f(-x) then function is called to be even.
A). f(x) = ∛8x
f(-x) = ∛8(-x) = (∛8)(∛(-x) = 2∛(-x)
Therefore f(x) ≠ f(-x)
So function is not an even function.
B). [tex]f(x)=log_{9}x^{6}[/tex]
[tex]f(-x)=log_{9}(-x)^{6}[/tex]
[tex]=log_{9}(x)^{6}[/tex]
f(x) = f(-x)
So this function is even.
C). [tex]f(x)=\frac{1}{x^{8}+7x^{7}}[/tex]
[tex]f(-x)=\frac{1}{(-x)^{8}+7(-x)^{6}}[/tex]
= [tex]\frac{1}{x^{8}+7x^{6}}[/tex]
f(x) = f(-x)
Therefore given function is even.
D). f(x) = [tex]e^{x^{8}-x }[/tex]
[tex]f(-x)=e^{(-x)^{8}-(-x)}=e^{x^{8}+x}[/tex]
Therefore f(x) ≠ f(-x)
So the given function is not even.
E). f(x) = |8x| - 3
f(-x) = |8(-x)| - 3
= |8x| - 3
f(x) = f(-x)
Therefore, function is even.
F). [tex]f(-x)= -9(-x)^{10}+5(-x)^{4}-12(-x)[/tex]
[tex]f(-x)= -9(x)^{10}+5(x)^{4}+12(x)[/tex]
f(x) ≠ f(-x)
Therefore the given function is not an even function.
Options B, C and E are even functions.
