
Find the complete solution set for the inequation ?
(a)
(b)
(c)
(d)
Answer
480.9k+ views
Hint: We start solving the problem by finding the interval for all values of x at which the given inequation is defined first. We use the property that for a function is defined only if for the function . We then use the property to find the interval for the values of x at which the function can be defined. We then find take the inequation and make the necessary calculations and use the property that if the inequality is defined as and , then the solution set of the inequality is to find the required solution set.
Complete step by step answer:
According to the problem, we need to find the complete solution set of the inequation .
Let us first find the value for which the given inequation is defined.
We know that for a function is defined only if .
So, we have .
.
---(1).
We know that the is a polynomial and we can see that all of its values should be greater than zero as we know that the value of the .
So, we have .
.
---(2).
The common interval of x for which the given inequation is defined will be the intersection of the values of x obtained in equations (1) and (2).
So, the inequation is defined on ---(3).
Now, let us find the solution set for the inequation .
.
.
.
.
.
.
---(4).
We know that if the inequality is defined as and , then the solution set of the inequality is . Using this we get the solution set for inequality in equation (4) as .
From equation (3), we remove the values of x which were not satisfying the interval to get the complete solution set.
So, we get the solution set for the inequality as .
So, the correct answer is “Option d”.
Note: We should not consider negative square roots while finding the solution set of the given inequalities as it will not always be true which we can see in this problem. We can also solve this problem by drawing the plots of and as shown below.
From this plot we can see that the values of lies below the line in the interval .
Complete step by step answer:
According to the problem, we need to find the complete solution set of the inequation
Let us first find the value for which the given inequation is defined.
We know that for a function
So, we have
We know that the
So, we have
The common interval of x for which the given inequation is defined will be the intersection of the values of x obtained in equations (1) and (2).
So, the inequation
Now, let us find the solution set for the inequation
We know that if the inequality is defined as
From equation (3), we remove the values of x which were not satisfying the interval
So, we get the solution set for the inequality as
So, the correct answer is “Option d”.
Note: We should not consider negative square roots while finding the solution set of the given inequalities as it will not always be true which we can see in this problem. We can also solve this problem by drawing the plots of

From this plot we can see that the values of
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