Equate the functions for minimum value of x.
[tex]\begin{gathered} f(x)=g(x) \\ \frac{1}{2}(2)^x=5x+2 \\ (2)^x=10x+4 \end{gathered}[/tex]
Check for x = 5,
[tex]\begin{gathered} (2)^5=10\cdot5+4 \\ 32<54 \end{gathered}[/tex]
For x = 6,
[tex]\begin{gathered} (2)^6=10\cdot6+4 \\ 64=64 \end{gathered}[/tex]
So for x = 6, the value of function f(x) and g(x) is equal and for values more than 6, the function f(x) is greater than function g(x).
Answe: x = 6
