If x is satisfied the inequality logx+3(x2−x)<1, the x may belongs to the set?
A) x∈(−3,−2)
B) x∈(−1,3)
C) x∈(1,3)
D) x∈(−1,0)
The answer is A), C) and D) for your reference
A)
B)
C)
D)
The answer is A), C) and D) for your reference
1 Answer
I got
Explanation:
By the definition of the logarithm, we have:
x2−x<(x+3)1
x2−x<x+3
x2−2x−3<0
Solving like an equation:
x2−2x−3=0
(x−3)(x+1)=0
x=3or−1
If we select a test point, say
02−2(0)−3<0√
However, if we use
x2−x>0
x2−x=0
x(x−1)=0
x=0or1
If we repeat the process with test points, we realize that the solution is
Now, we must also guarantee that
The answer is therefore :
x∈(−3,−2)∪(−1,0)∪(0,3)
A graphical verification yields the same results.
Hopefully this helps!