Answer to Question #100233 in Algebra for Jake

Question

Find the domain and range of f(x)=3/×^2+2

Answer 1

$f(x)= \cfrac{3}{x^2}+2$ .

Given that x is in the denominator, it cannot be equal to 0.

So, the domain of this function is $x \in (- \infty, 0)∪(0; + \infty)$.

The value $\cfrac{3}{x^2}$ could not be less than 0 because $x^2 >0$ for all x.

The value  $\cfrac{3}{x^2}$ could not be equal 0.

All of theese means that value $\cfrac{3}{x^2}+2 > 2$ for all x.

So, the range of $f(x)$ is $(2, + \infin )$ .

Answer: Domain is $(- \infty, 0)∪(0, + \infty)$ , range is $(2, + \infin )$ .