Find the domain and range of the function

Question:

Find the domain and range of the function

$F: R \rightarrow R: f(x)=x^{2}+1$

 

Solution:

Since the function $f(x)$ can accept any values as per the given domain $R$, therefore, the domain of the function $f(x)=x^{2}+1$ is $R$.

The minimum value of $f(x)=1$

$\Rightarrow$ Range of $f(x)=[-1, \infty]$

i.e range $(f)=\{y \in R: y \geq 1\}$

Ans: dom $(f)=R$ and range $(f)=\{y \in R: y \geq 1\}$

 

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