Answer:
x = 6
Explanation:
As the function f(x) is an exponencial function, it will grow faster than g(x), that is a linear function.
For small values of x, we have that f(x) < g(x). For example:
f(1) = 1/2 * 2 = 1
g(1) = 5*1 + 2 = 7
f(2) = 1/2 * 4 = 2
g(2) = 5*2 + 4 = 14
So we just need to check some integer values and see when f(x) will be bigger than g(x). It will not be a big value, as the exponencial function grows very fast.
For x = 5, we have:
f(5) = 1/2 * 32 = 16
g(5) = 5*5 + 4 = 29
For x = 6, we have:
f(6) = 1/2 * 64 = 32
g(6) = 5*6 + 4 = 34
For x = 7, we have:
f(7) = 1/2 * 128 = 64
g(7) = 5*7 + 4 = 39
So the largest integer value of x for f(x) ≤ g(x) is x = 6.
Another way to solve this is by plotting both equations, and then checking where they cross, that is, where f(x) = g(x).