Grade 9Algebra
PLEASE help me with this question Q. Find Domain and Range of – f(x)= (x^2 -3x +4) / (x^2 +3x+4) Thank you!
PLEASE help me with this question
Q. Find Domain and Range of –
f(x)= (x^2 -3x +4) / (x^2 +3x+4)
Thank you!
2 Answers
Ajay
Lets check the denominator = x^2 + 3x + 4 . Domain will be R- {values for which denominator is zero}
Here D = 9-16 is negative which implies it is never zero.
Hence Domain is R
To find Range let y = (x^2 -3x +4) / (x^2 +3x+4)
Experessing this in terms of x we can simplify
(y-1)x^2 + 3(y+1) x + 4(y-1) = 0
Since x is always real D for this quandratic equation should be greater than or equal to zero
9(y-1)^2 – 16(y-1)^2 >= 0
7y^2-50y+7
(y-7)(7y-1)
this is true for 1/7
Ajay
9(y-1)^2 – 16(y-1)^2 >= 0
Implies
7y^2-50y+7 less tan equal to zero
(y-7)(7y-1) is less than equal to zero
y is between 1/7 and 7.
This is required domian
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