What is the domain and range of $y=ln(x^2)$ ?

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Answer 1 · 2017-04-09T14:02:19

Domain for $y=ln(x^2)$ is $x in R$ but $x!=0$ , in other words $(-oo,0)uu(0,oo)$ and range is $(-oo,oo)$ .

We cannot have logarithm of a number less than or equal to zero. As $x^2$ is always positive, only value not permissible is $0$ .

Hence domain for $y=ln(x^2)$ is $x in R$ but $x!=0$ , in other words $(-oo,0)uu(0,oo)$

but as $x->0$ , $ln(x^2)->-oo$ , $y$ can take any value from $-oo$ ao $oo$ i.e. range is $(-oo,oo)$ .

What is the domain and range of y=ln(x^2)y=ln(x^2)?