Please explain range........with some moderate examples from the basics
Thnk u
Shubham
341Let f: A → B.
Then the range of f, is a sub-set of B. It consists of those elements b ε B such that there exists a ε A, satisfying f(a)=b
For example f(x) = 2x. The range of f is (0,∞).
or f(x) = x + 1/x, x ε R, x≠0. You can try and prove that the range is
R - (-2,2).
There is no one-case-fits-all way to go about finding the range. So, you could post some problems where you need help.
1suppose we are asked to prove that xx+1 is invertible. then how do we do it.... without using graphs.... plz tell me....
1708$\boldsymbol{Ans:}$\Rightarrow$ Let $f(x)=\frac{x}{1+x}=\frac{1+x-1}{1+x}=1-\frac{1}{1+x}$\\\\ If This function is Invertable Then It must be one-to-one and onto. and Co-domain=range.\\\\
1In f(x)=2x if we subsititue x is -1/2 thn.....we get.....2-1/2 and tht becomes 1/21/2 so why isits range (0 , ∞) ?
71from the graph of an exponential FUNCTION..see that it never goes below the x axis or tends to meet at infinity... so range is 0 TO infinity.... you can see it logically too.
1for x>=0,2x>=1. [equality holds for x=0]
for x<0,0<2x<1.
clearly 2x is always >0
so range is (0,∞)