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Relations and Functions
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Show that $\frac{1}{\sin^3x}+\cot x+\frac{1}{x^5}+x^3 $ is an odd function.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q10
p3
math
sec-a
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Jan 23, 2013
by
meena.p
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Show that the relation R on N x N defined by $(a,b)R(c,d)\;\Leftrightarrow \; a+d = b+c $is an equivalence relation.
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Let $ \int : {R\; \rightarrow \;R}$ be a function defined by $ f(x) = x^2-3x+4,$ for all $x \in R ,$ find the value of $f^{-1}(2)$.
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Let $f:R_+\rightarrow[-5,\infty) $ given by $f(x)=9x^2+6x-5.$ show that f is invertiable with $ f^{-1}(y)=\frac{\sqrt{y+6}-1}{3}.$
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If $f(x)=log \big(\frac{1+x}{1-x}\big)$ show that $f(x)+f(y)=f \big(\frac{x+y}{1+xy}\big)$
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Show that the relation "“congruence modulo 2"” on the set Z (set of integers) is an equivalence relation. Also find the equivalence class of 1.
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Jan 23, 2013
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