I don't know if it is the right platform to ask this. (Forgive me if not.) But I need to study about inequalities and inequality solving methods from a very basic level. I can not figure out under which book title (Algebra Or Calculus) inequality chapter comes. That's why it became very much difficult to find right book on google search. Please suggest me some books of inequality for the elementary study.
$\boldsymbol{Very}$ $\boldsymbol{Basic}\boldsymbol{Level}$$\Longrightarrow$I
am studying differential calculus for postgraduate entrence exam.I need
to find domain and range of given funtion.This is the topic where
i need to get acquainted with the methods of sloving inequality equation
for x(say)
Here are few problems$\Longrightarrow$1. $\frac{1+(log_{a}x)^{2}}{1+log_{a}x}\succ1$,0$\prec a\prec1$
3sin2x$\succ$sinx + cosx+1
log$_{\sqrt{2x^{2}-7x+6}}$($\frac{x}{3})\succ0$
4.log$_{3}\frac{|x^{2}-4x|}{x^{2}+|x-5|}\geq0$
Here i need to find the interval where x may belong.So Please suggest
me a book that helps in solving every kind of equation like quadratic,transcedental,exponential,logrithmic
etc.
Answer
You should try HOW TO LEARN CALCULUS OF ONE VARIABLE BY J.D. GHOSH IT HAS EXACTLY WHAT YOU NEED. It contains very sharp methods of solving inequality
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