I need to know on the following: h(x)= 1.95x +72.85 Invalid value for the domain? And why? also Invalid value for the range and why?

Expert Answers
hala718 eNotes educator| Certified Educator

The question depends on what h(x) refers to:

For example:

if h is height, then h can not be negative value.

Then the domain is h >= 0 , OR [0, inf]

To calculate the range:

h(x) = 1.95x + 72.85 >= 0

==> 1.95 x >= -72.85

Now divide by 1.95:

==> x >= -72.85/1.95

==> x >= -37.36 (approx)

Then the range = ( -37.36, inf)

neela | Student

h(x) = 1.95x+72.85

The domain here is  the set of x values  for which the range 1.95x+72.85 is real.

In this case for any value of x , the range 1.95 x +72.85 is real. So the d0main of values is the set of values x takes is the set { -ifinity , infinity} and the range  1.92x+72.75 is the set of values ,( infinity , infinity} or all the real values.

Invalid domain: f(x) = 1/(x-a) is a fuction where x is not equal to a. So x = a is invalid  domain. Therefore the domain is excluding zero Or the domain is R-{a}.

f(x) = sqrt(x^2- 14), the domain is ivalid if  x < 4 and x >4. So the domain -4 <x <4  is invalid. The valid domain is x<-4  or  x>4.