find the domain of the function f(x) = x^2+3x+5/x^2-5x+4 sketch the graph of the function f(x) = |x+1|
Answers
EXPLANATION.
(1) = Domain of the function f(x) = x² + 3x + 5/x² - 5x + 4.
⇒ f(x) = x² + 3x + 5/x² - 5x + 4.
factorizes denominator into middle term split we get,
⇒ x² - 5x + 4.
⇒ x² - 4x - x + 4 = 0.
⇒ x ( x - 4 ) -1 ( x - 4).
⇒ ( x - 1 ) ( x - 4 ).
⇒ x² + 3x + 5/(x - 1)(x - 4) = 0.
as the denominator is ≠ 0.
if numerator is equal to zero then values = 0.
if denominator is equal to zero then values not exists.
so, ( x - 1 ) and ( x - 4 ) ≠ 0.
so, domain is all real number except 1 and 4.
Domain = x ∈ R - { 1,4}.
(2) = Draw the graph of the function f(x) = | x + 1 |.
if the number is insides the modes there is two cases exist.
(1) put the value of x = 0 in equation,
⇒ f(x) = 1.
(2) = put the value of y = 0 in equation,
⇒ f(x) = x + 1 = 0.
⇒ f(x0 = x = -1.
their co-ordinate are = ( 0,1) and ( -1,0).
