Prove that if the domain of definition o...

Prove that if the domain of definition of the function f(x) is symmetrical with respect to x=0, then f(x) + f(-x) is an even function and f(x)-f(-x) is an odd one.

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IA MARON-INTRODUCTION OF MATHEMATICAL ANALYSIS-Additional Problems

Investigating the domain of definition of functions. (a) Solve the i...
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Prove that the product of two even or two odd functions is an even fun...
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Prove that if the domain of definition of the function f(x) is symmetr...
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Prove that any function f(x) defined in a symmetrical interval (-l, l)...
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Extend the function f(x)=x^2 + x defined on the interval (0,3) onto th...
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Prove theat the Drichlet function lambda(x) is a periodic one but has ...
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Prove that if the function f(x)=sin x+cos a x is a periodic, than a is...
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Prove that the sum of two functions increasing on a certain open inter...
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Give an examole of non-monotonic functions that has an inverse.
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Determine the inverse function and its domain of definition, if (a) y=...
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Show that the equation x^(2)+2x+1+sqrtx has no real roots.
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Prove that if the graph of the function y=f(x), defined throughout the...
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Let the sequence xn converge and the sequence yn diverge. What can be ...
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Let the sequences xn and yn diverge. Can one assert that the sequences...
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Let alpha(n) be an interior angle of a regular n-gon (n=3,4,...). Writ...
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Prove that from underset(n to oo) xn=a a it follows that underset(n t...
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Prove that if the sequence {an//bn} {bn gt 0} is monotonic, then the s...
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Prove the existence of limits of the following sequences and find them...
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Prove that if the function f(x): (1) is defined and monotonic on the i...
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Let the function y =f(x)be continuous on the interval [a, b], its rang...
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