Pure Math related to function
2012-09-24 9:08 am
Let f be function defined on (-j,j), where j is real number. show that ( a) g(x)=f(x)+f(-x) is an even function. (b). h(x)=f(x)-f(-x) is an odd function. (c). Consider the function. I. F(x)=a即x次方(a bigger than 0). II. F(x)= (1+x)即n次方. n is integer. Ps. Use answer of (ab)find function of g(x). And h(x)
回答 (1)
2012-09-25 5:17 am
✔ 最佳答案
(a) g(-x) = f(-x) + f(x) = g(x) and so g(x) is an even function(b) h(-x) = f(-x) - f(x) = -[f(x) - f(-x)] = -h(x) and so h(x) is an odd function
(c)(i) f(x) = a^x
g(x) = a^x + 1/a^x , h(x) = a^x - 1/a^x
(ii) f(x) = (1 + x)^n
g(x) = (1 + x)^n + 1/(1 + x)^n
h(x) = (1 + x)^n - 1/(1 + x)^n
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