Question

If the range of f(x) = ^mx and the range of g(x) = m ^ x are the same, which statement is true about the value of m?

a) m can only equal 1.
b) m can be any positive real number.
c) m can be any negative real number.
d) m can be any real number.

Answer 1

Explanation:

Given that the range of f(x) = ^mx and the range of g(x) = m ^ x are the same

i.e. a^mx and m^x will have the same range.

If m =1, then we have second function as 1 and hence cannot be correct

If m <0 and a>0 then I function will be positive while second function negative. So range cannot be equal

If m is any real number then same argument for negative number makes this false.

If m>0, and a>0 then a^mx and also m^x will be positive and hence range is R+ including 0

Answer 2

b) m can be any positive real number too easy XD

Explanation:

Hope this helps!! :D