Looking at the graph will easily give the answer, but if you want to do it with algebra:
Remember that the domain is all possible values of x. Also note that anything under a square root can't be negative. To solve this problem I would take the square root away for a moment and set what's left to be >= 0.
This gives:
-4x + 3 >= 0
Solving:
-4x + 3 >= 0
-4x + 3 - 3 >= 0 - 3
-4x >= -3
(-4x) / -4 <= -3 / -4 Note: >= flipped to <= due to a division by a negative number
x <= 3/4
This tells us that x has to be less than or equal to 3/4 for this to be a valid statement. The reason we can come to this conclusion is because we NEED the value under the radical sign to be positive. You can't take the square root of a negative number because NO number squared is negative.
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Verified answer
Looking at the graph will easily give the answer, but if you want to do it with algebra:
Remember that the domain is all possible values of x. Also note that anything under a square root can't be negative. To solve this problem I would take the square root away for a moment and set what's left to be >= 0.
This gives:
-4x + 3 >= 0
Solving:
-4x + 3 >= 0
-4x + 3 - 3 >= 0 - 3
-4x >= -3
(-4x) / -4 <= -3 / -4 Note: >= flipped to <= due to a division by a negative number
x <= 3/4
This tells us that x has to be less than or equal to 3/4 for this to be a valid statement. The reason we can come to this conclusion is because we NEED the value under the radical sign to be positive. You can't take the square root of a negative number because NO number squared is negative.
I hope this helps!
I'll assume you mean y=â(-4x+3).
-4x + 3 ⥠0
3 ⥠4x
3/4 ⥠x
x ⤠3/4
I'm not sure what 3- -4x+3â¥0 -3 means.
Also, when you divided by -4 in this step -4x/-4â¥-3/-4, you neglected to change the direction of the inequality.
-4x+3>=0
-4x>=-3
4x<=3
x<=3/4