If the range of f(x)= sq rt mx and the range of g(x)=m sq rt x are the same, which statement is true about the value of m? m can only equal 1. m can be any positive real number. m can be any negative real number. m can be any real number.

The  statement which is true about the value of m is:

We are given two functions f(x) and g(x) as:

and g(x) is given by:

Now, we know that:

The domain of a square root function is always greater than or equal to zero.

By function f(x) we have:

so, the range is the set of all the positive real numbers.

Now, by looking at the function g(x) we have:

but m could be positive or negative,

This means that the range of the function g(x) is the set of all the real numbers.

But it is given that:

Range of both the functions are equal.

This means that:

for all the values of x.

This means that m has to be positive.

i.e. m≥0

Hence, the value of m has to be the set of all the positive real numbers.

m can only be equal to 1

Step-by-step explanation:

Range of f(x) = Range of g(x)

Squaring both sides,

m(m-1) = 0

m cannot be 0.

So, m - 1 = 0 and m = 1.

So, m can boly be 1.