function ...

[danielvnl]

Give the condition to the domain and range of the function f_(x)=x²

a) to be an injective function

b) to be a bijective function

My answer

a) If f_{(x) :} R --> R to the function f_(x)=x² so we have an injective function

b) If f_{(x) :} R₊ --> R₊ to the funtion f_(x)=x² so we have a bijective function

Am I right ??

 

[HallsofIvy]

Give the condition to the domain and range of the function f_(x)=x²

a) to be an injective function

b) to be a bijective function

My answer

a) If f_{(x) :} R --> R to the function f_(x)=x² so we have an injective function

b) If f_{(x) :} R₊ --> R₊ to the funtion f_(x)=x² so we have a bijective function

Am I right ??

Not for (a). In order to be "injective" a function has to be "one to one": is \(\displaystyle x\ne y\) then \(\displaystyle f(x)\ne f(y)\).
Here, \(\displaystyle 2\ne -2\) but \(\displaystyle f(2)= 4= f(-2)\).

 

[danielvnl]

So to a) the correct is R₊ --> R ????

 

[HallsofIvy]

So to a) the correct is R₊ --> R ????

That's one possible answer. Other are \(\displaystyle R_+\to R\), \(\displaystyle R_+\to R_+\), and \(\displaystyle R_-\to R_+\).