SOLUTION: f(x)=2x^2-1 _______ x^2 a f(5) b f(-5) c f(-x)

Question 1031765: f(x)=2x^2-1
_______
x^2
a f(5)
b f(-5)
c f(-x)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
(a)

Replace EVERY copy of x with 5

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(b)

Replace EVERY copy of x with -5

See note below

Note: squaring something like -5 yields a positive result since (-5)^2 = (-5)*(-5) = +25

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(c)

Replace EVERY copy of x with -x

Now because (based on the note above) this means that we end up with

which is the same as the original function. Only the left side is different. Because , for all values of x in the domain of f(x), this means that f(x) is an even function. It is symmetric with respect to the y axis.
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