g(x)=square root of x^2-4x
show me the steps
Thank You :)
show me the steps
Thank You :)
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I assume that you are working with only real numbers. If that is the case, then it is clear that the number under the square root must be positive or zero. Otherwise it is meaningless in the real number system. So you have:
g(x) = sqrt(x^2 - 4x)
=> (x^2 - 4x) >= 0
=> x(x-4) >= 0
Now the product >= 0 only if both of them are positive or both of them are negative. Using this gives:
i. Both positive:
x >=0 and (x-4) >= 0
=> x>=0 and x>=4
The second condition takes care of the first. Hence the solution in this case is: x>=4
ii. Both negative:
x<=0 and (x-4) <=0
=> x<=0 and x<=4
The first condition takes care of the second. Hence the solution in this case is: x<=0.
Thus the domain D for the function g(x) is: D = (-inf,0] U [4,inf)
where (,) indicates that the end point is not included and [,] indicates that the end point is included.
g(x) = sqrt(x^2 - 4x)
=> (x^2 - 4x) >= 0
=> x(x-4) >= 0
Now the product >= 0 only if both of them are positive or both of them are negative. Using this gives:
i. Both positive:
x >=0 and (x-4) >= 0
=> x>=0 and x>=4
The second condition takes care of the first. Hence the solution in this case is: x>=4
ii. Both negative:
x<=0 and (x-4) <=0
=> x<=0 and x<=4
The first condition takes care of the second. Hence the solution in this case is: x<=0.
Thus the domain D for the function g(x) is: D = (-inf,0] U [4,inf)
where (,) indicates that the end point is not included and [,] indicates that the end point is included.