Answer:
g(x) = -f(x+3)
f(x) = -g(x-3)
Step-by-step explanation:
Transformations
Function f can be obtained by knowing function g and vice-versa.
Suppose we know the expression of function f. If we reflect f across the x-axis, we get function g but displaced 3 units to the right.
Thus, we only have to translate the reflected f 3 units to the left:
g(x) = -f(x+3)
Similarly, if g(x) is reflected across the x-axis and translated by 3 units to the right, we get f(x), thus:
f(x) = -g(x-3)
