Hello!
The answer is:
C. [tex]F(x)=2^{x}-1[/tex]
Why?
In order to find the correct option, we need to substitute/evaluate the given values of "x" into each function.
Substituting into the first equation, option A:
[tex]F(x)=3^{x} \\F(3)=3^{3}=27\\F(3)=3^{4}=81[/tex]
... and so.
We can see that the option A is not the correct option since the obtained values do not match with the given values.
Substituting into the second equation, option B:
[tex]F(x)=3x\\F(3)=3*3=9\\F(4)=3*4=12\\[/tex]
... and so.
We can see that the values obtained from the function do not match with the given values, so the option B is not correct.
Substituting into the third equation, option C:
[tex]F(x)=2^{x}-1\\F(3)=2^{3}-1=8-1=7\\F(4)=2^{4}-1=16-1=15\\F(5)=2^{5}-1=32-1=31\\F(7)=2^{7}-1=128-1=127\\F(8)=2^{8}-1=256-1=255\\[/tex]
So, since all the obtained values match with the given values, we can conclude that the correct option is the option C.
Have a nice day!
