- #1
ajassat
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I was working on the following problem from a textbook. The textbook has no answer. I have included my solution - I am not sure whether it is correct Any ideas and or solutions? (guidance)
Question:
Suppose that f is any function with domain (-infinity, +infinity)
a) Does the function g defined by g(x) = f(x) + f(-x) have any special symmetry?
My solution
A function f which satisfies:
f(-x) = -f(x) is symmetrical about the horizontal axis. This is also:
f(x) + f(-x) = 0
or we could substitute values of x giving non zero solutions for:
f(x) + f(-x) = g(x) (some other function)
Therefore g(x) = f(x) + f(-x) has symmetry about horizontal axis?
Any guidance appreciated.
Regards,
Adam
Question:
Suppose that f is any function with domain (-infinity, +infinity)
a) Does the function g defined by g(x) = f(x) + f(-x) have any special symmetry?
My solution
A function f which satisfies:
f(-x) = -f(x) is symmetrical about the horizontal axis. This is also:
f(x) + f(-x) = 0
or we could substitute values of x giving non zero solutions for:
f(x) + f(-x) = g(x) (some other function)
Therefore g(x) = f(x) + f(-x) has symmetry about horizontal axis?
Any guidance appreciated.
Regards,
Adam