Solve each of the following equation
1 answer:
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The statements that are true about the intervals of the continuous function are Options 2, 4 and 5
- f(x) ≤ 0 over the interval [0, 2].
- f(x) > 0 over the interval (–2, 0).
- f(x) ≥ 0 over the interval [2, ).
Looking at the values given, the intervals which satisfies the condition are known to be:
f(x)<=0 over the interval [0,2]
f(x)>0 over the interval (-2,0)
f(x)>=0 over the interval [2,∞)
Because:
Since the table with x and f(x) values, we have to examine analyze the table and see the each option that is in line with f(x) or not .
Examine the values of x that is from -3 to 3, the f(x) values are both positive and negative . hence f(x)>0 is false over the interval (-∞,3)
Looking at the the interval from 0 to 2, the f(x) values are 0 and negative. Hence, f(x)<=0 over the interval [0,2]
When you look over the interval (-1,1), the f(x) values are said to be both positive and negative and as such, f(x)<0 is false over the interval (-1,1)
When you look at the interval (-2,0) , the f(x) is positive and as such, f(x)>0 over the interval (-2,0)
Looking at the interval [2,∞), f(x) is positive and as such, f(x)>=0 over the interval [2,∞)
Therefore, Option 2, 4 and 5 are correct.
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As X' is the reflected point of X(0,3) , so the x co ordinate of X' = 0+8 =8 and here y co ordinate remains same.
So, X'= (8,3)
Like that way, Y' is the reflected point of Y(2,0) and Z' is the reflected point of Z(4,2)
As the point Z is lying on the line x=4 and the reflection is also across that line, so both Z and Z' represent same point.
Y'= (2+4, 0) = (6, 0)
Z' = (4, 2)
Option C is correct option.
Step-by-step explanation:
We need to find the solution of
The given inequality becomes undefined when x = 1 because the denomiator is: 1-x and if x = 1 then it becomes 1-1 = 0 and anything divided by zero is undefined.
So, all values other than 1 are included in the solution of the given inequality.
So, solution is: x<1 or x>1 but x≠1
So, Option C is correct because all numbers are included in number line except 1. An unfilled circle on 1 shows that it is not included in the solution. Rest of numbers are included.
Option C is correct option.
Keywords: Solving inequalities
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