Final answer:
After evaluating both functions f(x) and g(x) at x = 4, it is evident that f(4) = 5 and g(4) = 10, showing that the functions are not equivalent.
Step-by-step explanation:
To show that the functions f(x) and g(x) are not equivalent, we can evaluate each function at the same value of x and compare the results. Let's choose x = 3 as a suitable value since it will simplify the expressions.
For f(x) = 2(x-3) + 3(x-3), we substitute x = 3:
f(3) = 2(3-3) + 3(3-3) = 2(0) + 3(0) = 0 + 0 = 0
For g(x) = 5(2x-6), we substitute x = 3:
g(3) = 5(2*3-6) = 5(6-6) = 5(0) = 0
In this case, evaluating both functions at x = 3 yields the same result, 0. However, to conclusively show that the two functions are not equivalent, we need to choose a different value of x where the outputs differ. Let's try x = 4:
f(4) = 2(4-3) + 3(4-3) = 2(1) + 3(1) = 2 + 3 = 5
g(4) = 5(2*4-6) = 5(8-6) = 5(2) = 10
Here, we can see that f(4) ≠ g(4), which proves that the functions f(x) and g(x) are not equivalent.