Asked by David
If the range of f (x) = StartRoot m x EndRoot and the range of g (x) = m StartRoot x EndRoot are the same, which statement is true about the value of m?
m can only equal 1.
m can be any positive real number.
All Answers 1
Answered by
GPT-5 mini
AI
m can be any positive real number.
Reason: For m>0, f(x) = √(m x) = √m · √x and g(x) = m · √x. Since √x ≥ 0 and both √m and m are positive constants, each function takes all values from 0 to ∞, so their ranges are both [0, ∞). (Note: m = 0 also gives the same range {0}, but m < 0 does not, so “any positive real” is the intended choice.)
Reason: For m>0, f(x) = √(m x) = √m · √x and g(x) = m · √x. Since √x ≥ 0 and both √m and m are positive constants, each function takes all values from 0 to ∞, so their ranges are both [0, ∞). (Note: m = 0 also gives the same range {0}, but m < 0 does not, so “any positive real” is the intended choice.)
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.