Question

Find the domain and range of the function f(x)= x 2 + 4

Answer 1

Answer:

domain is R

range is

(4, infinity)

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO DETERMINE

The domain and range of the function

$f(x) = {x}^{2} + 4$

EVALUATION

DOMAIN

The function is well defined for every value real value x

So the required Domain of the function is $\mathbb{R}$

RANGE

Let

$y \: = {x}^{2} + 4$

$\implies \: {x}^{2} = y - 4$

$\implies \: x = \sqrt{ {y} - 4 }$

Now

$x \in \mathbb{R} \: \: if \: \: \: {y} - 4 \geqslant 0$

Hence

$x \in \mathbb{R} \: \: if \: \: \: {y} \geqslant 4$

So the required Range is

$= \{x \in \: \mathbb{R} \: : \: x \geqslant 4 \: \}$

$= [ \: 4, \infin \: )$