Question

For function f, it is known that f(3) = 0 and f(6) = -4. The function g is given by g(x) = f(x-4), which of the following must be a solution to g(x) = 0?

Option 1: x = 0
Option 2: x = 4
Option 3: x = 7
Option 4: x = 10

Answer 1

To solve for g(x) = 0, we utilize the fact that g(x) = f(x-4) and f(3) = 0. Setting x-4 = 3 and solving for x gives us x = 7, making option 3 the correct solution.

Step-by-step explanation:

To determine which option is a solution to g(x) = 0, we need to recall that g(x) is defined in terms of the function f, specifically g(x) = f(x-4). We know that f(3) = 0. To find out when g(x) will be zero, we can set up the equation x-4 = 3 because we want the input to f inside the definition of g to be 3 in order to get the output of 0. Solving for x, we get:

• x - 4 = 3
• x = 3 + 4
• x = 7

Therefore, option 3, x = 7, must be a solution to g(x) = 0. When x = 7, then g(7) = f(7 - 4) = f(3), and since f(3) = 0, it means g(7) = 0 as required.