Question

How do you find the domain and range of `f(x)=sqrt (x+7)/(x^2+7)`?

Answer 1

domain`RR={x:x inRR,x>=(-7)}`and range`RR={y:y inRR,y>=0}`

Explanation:

Suppose,y=`f(x)=sqrt(x+7)/(x^2+7)`
If `x<(-7),`the mentioned equation can not be definable.

`sqrt(x+7)/(x^2+7)`=indefinable,when `x<(-7.)` `color(brown)[[As.sqrt(-x in RR)=(INDEFINABLE)]]`

Hence,Domain`RR=color(red){{x:x inRR,x>=(-7)}`

For the value of domain set,range of the equation will be greater than or equal `0`

*So,Range`RR=color(blue){{y:y inRR,y>=0}` *