Answer:
To find the value of x where f(x) < g(x), we need to set the two functions equal to each other and solve for x:
3^x = 2x + 5
We can't solve this equation algebraically, so we'll need to use trial and error or graphing to find the solution.
Using trial and error, we can substitute different values of x into the equation and see which one makes f(x) less than g(x):
- If x = -1, then f(x) = 3^(-1) = 1/3 and g(x) = 2(-1) + 5 = 3. Therefore, f(x) < g(x) when x = -1.
- If x = 2, then f(x) = 3^2 = 9 and g(x) = 2(2) + 5 = 9. Therefore, f(x) is not less than g(x) when x = 2.
- If x = -3, then f(x) = 3^(-3) = 1/27 and g(x) = 2(-3) + 5 = -1. Therefore, f(x) is not less than g(x) when x = -3.
- If x = -4, then f(x) = 3^(-4) = 1/81 and g(x) = 2(-4) + 5 = -3. Therefore, f(x) is not less than g(x) when x = -4.
Therefore, the solution is x = -1.