The value of x that satisfies (fog)(x) = -8 is: x = 4
To find the value of x when (fog)(x) = -8, we need to follow these steps:
Identify the composition of functions: (fog)(x) means applying function f followed by function g to x.
Solve for the value of g(x): We know that (fog)(x) = -8. Since we need to find x, we need to isolate x. Therefore, we need to find the value of g(x) that makes f(g(x)) = -8.
Apply function g: We don't have the explicit formula for function g, but we have a table of values. Look for the value of y (g(x)) that, when plugged into function f, results in an output of -8.
Solve for x: Once you find the value of y that makes f(y) = -8, find the corresponding x-value in the table. This x-value will be the solution to the equation (fog)(x) = -8.
Analyzing the table:
We need to find a value of y in the g(x) column that makes f(y) = -8.
Looking at the f(x) column, we see that f(4) = -8.
Therefore, we need to find the value of x in the g(x) column that corresponds to y = 4.
In the g(x) column, y = 4 corresponds to x = 4.
Therefore, the value of x that satisfies (fog)(x) = -8 is: x = 4