Respuesta :
So we are given two functions:
[tex]f(x)=\sqrt{mx}\\g(x)=m\sqrt x[/tex]
The range of the function g is the following
[tex]x\geq 0 [/tex].
The range of the function f is:
[tex]m\times x\geq 0 [/tex]
Since the two ranges are equation, we deduce that the value of m is positive.
Otherwise the solution of the above inequality would be
[tex]x\leq 0 [/tex]
which is not the same as the first inequality.
[tex]f(x)=\sqrt{mx}\\g(x)=m\sqrt x[/tex]
The range of the function g is the following
[tex]x\geq 0 [/tex].
The range of the function f is:
[tex]m\times x\geq 0 [/tex]
Since the two ranges are equation, we deduce that the value of m is positive.
Otherwise the solution of the above inequality would be
[tex]x\leq 0 [/tex]
which is not the same as the first inequality.
Answer:
[tex]m[/tex] must be positive to have equal range between these functions.
Step-by-step explanation:
The given functions are
[tex]f(x)=\sqrt{mx}[/tex] and [tex]g(x)=m\sqrt{x}[/tex]
If we analyse each function, we'll notice that the range of [tex]f(x)[/tex] is all real numbers greater of equal than zero, because a square root can't give negative values.
The second funcion as the same range, all number greater or equal than zero, because it can't give a negative numbers, so they are ranges are the same.
However, their domains are
[tex]D_{f}:mx\geq 0\\D_{g}: x\geq 0[/tex]
At this points, you may not notice the characteristic of [tex]m[/tex], notice that the range of [tex]g(x)[/tex] has to have a restriction for [tex]m[/tex], it must be greater or equal than zero, otherwise the ranges won't be the same.
Therfore, [tex]m[/tex] must be positive to have equal range between these functions.
