Set, Relation and FunctionHard
Question
f : R → R, f(x) = 
. If the range of this function is [-4, 3), Then find the value of |m + n| is :-
. If the range of this function is [-4, 3), Then find the value of |m + n| is :-Options
A.4
B.3
C.7
D.None
Solution
y = 
x2(y - 3) - mx + (y - n) = 0
ᐃ ≥ 0
m2 - 4(y - 3)(y - n) ≥ 0
m2 - 4y2 + 4(n + 3) y - 12n ≥ 0 ...(1)
4y2 - 4(n + 3)y + 12n - m2 ≤ 0
But - 4 ≤ y < 3
So (y + 4) (y - 3) ≤ 0
y2 + y - 12 ≤ 0 ...(2)
equation (1) and equation (2) should be similar
so
- n - 3 = 1
n = - 4; m = 0 |m + n| = 4
x2(y - 3) - mx + (y - n) = 0
ᐃ ≥ 0
m2 - 4(y - 3)(y - n) ≥ 0
m2 - 4y2 + 4(n + 3) y - 12n ≥ 0 ...(1)
4y2 - 4(n + 3)y + 12n - m2 ≤ 0
But - 4 ≤ y < 3
So (y + 4) (y - 3) ≤ 0
y2 + y - 12 ≤ 0 ...(2)
equation (1) and equation (2) should be similar
so
- n - 3 = 1
n = - 4; m = 0 |m + n| = 4
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