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.

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

Step-by-step explanation:

Hope this helps!! :D

Step-by-step 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

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is