FIND THE RANGE AND DOMAIN

Asked by vk1994 | 29th Apr, 2010, 11:45: AM

Expert Answer:

Dear Student,

The solution to your problem is as forllows -

 

therefore when x=3 or x=2, y is undefined.

=> Domain of f(x) =

 

For range,

Now as x is real, therefore y2+4y must be greater than or equal to zero.

=> y2+4y >= 0

=> y(y+4) >= 0

There are now three cases,

1) y >= 0 and y >= -4

=> y ∈ (0,infinity)

 

2) y >= 0 and y <= -4

This results in an empty set, as no y can be both greater than 0 and less than -4 simultaneously.
 

3) y <= 0 and y <= -4

=> y ∈ ( - infinity, -4)

Taking the union of the three sets obtained, we get the range of f(x) as,

range =

 

Regards Topperlearning.

Answered by  | 29th Apr, 2010, 12:30: PM

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