Question

Compare the functions f(x) = 2x® and g(x) = 3' by completing parts (a) and (b). (a) Fill in the table below. Note that the table is already filled in for X=3.

Answer 1

Find the corresponding values of f(x) for every value of x in the table, as shown below

$\begin{gathered} f(x)=2x^3 \\ f(4)=2*4^3=2*64=128 \\ f(5)=250 \\ f(6)=432 \\ f(7)=686 \end{gathered}$

Similarly, in the case of g(x),

$\begin{gathered} g(x)=3^x \\ g(4)=3^4=81 \\ g(5)=243 \\ g(6)=729 \\ g(7)=2187 \end{gathered}$

The values above are the answers to part (a)

(b) Notice that,

[tex]\begin{gathered} 128>81\Rightarrow f(4)>g(4) \\ 250>243\Rightarrow f(5)>g(5) \\ 432<729\Rightarrow f(6)Therefore, f(x) is sometimes less than g(x).