Question

Draw the graph and find the domain and range for the functions:

(i) f(x) = x² - 1
(ii) f(x) = |x² - 1|
(iii) f(x) = |x - 1|

Don't forget to attach the graph! No incomplete answers are allowed.
No spams!!​

Answer 1

Answer:

{ R }   ;   { R }    ;  { R }.

Step-by-step explanation:

For f( x ) = x^2 - 1 :-

      In functions we include on those function which have a real value( not imaginary ).

 Therefore, we solve on the same basis.

In the given f( x ) we have x^2 - 1, which will always be a real number for all x ∈ R.

 Thus, domain is ( ∞ , - ∞ ) or we say domain is { R } ( all real numbers ).

Let y = x^2 - 1

        ⇒ y = x^2 - 1      ⇒ y + 1 = x^2     ⇒ √( y + 1 ) = x

As x is a real number √( y + 1 ) must be a real number, for this y + 1 shouldn't be a -ve number   ⇒ y + 1 ≥ 0     ⇒ y ≥ - 1.

       Hence range of the given function is [ - 1 , ∞ ).

For f( x ) = | x^2 - 1 |

   Domain( as in the above question ) is { R }.

Let y = | x^2 - 1 |  

 This will always be a +ve number. So range is [ 0 , ∞ ).

For f( x ) = | x - 1 |

 A real-positive will be given( always ) for all real x(s). Therefore, domain is { R } and range is [ 0 , ∞ ).

Answer 2

Hope this will help you

Hope this will help youRegards