Answer:
The correct option is C.
Step-by-step explanation:
If a function is defined as
\(f(x)=a^x\)
where, a>0, then the range of the function is greater than 0.
\(a^x>0\) .... (1)
Option A: Using inequity (1),
\((2)^x>0\)
Multiply both side by 3.
\(3(2)^x>0\)
\(y>0\)
The range of first function is y>0. Therefore option A is incorrect.
Option B: Using inequity (1),
\((3)^x>0\)
Multiply both side by 2.
\(2(3)^x>0\)
\(y>0\)
The range of second function is y>0. Therefore option B is incorrect.
Option C: Using inequity (1),
\((2)^x>0\)
Multiply both side by -1.
\(-(2)^x<0\) \((\text{change the sign of inequality})\)
Add 3 on both the sides.
\(-(2)^x+3<3\)
\(y<3\)
The range of first function is y<3. Therefore option C is correct.
Option D: Using inequity (1),
\((2)^x>0\)
Subtract 3 from both the sides.
\(2^x-3>-3\)
\(y>-3\)
The range of second function is y>-3. Therefore option D is incorrect.
