Final answer:
To find the solutions to the equations f(x) = -x²-3 and g(x) = |x+4| -9, set the two equations equal to each other, isolate the absolute value expression, and solve for x in two separate cases based on the sign of x+4. The possible solutions are x = 1 and x = -7.
Step-by-step explanation:
To find the solutions to f(x) = g(x) where f(x) = -x²-3 and g(x) = |x+4| -9, we need to set the two equations equal to each other and solve for x.
First, we set the equations equal to each other: -x²-3 = |x+4| -9.
Next, we can solve for x by isolating the absolute value expression and solving two separate cases based on the sign of x+4. In one case where x+4 is positive, we remove the absolute value and solve for x. In the other case where x+4 is negative, we negate the absolute value expression and solve for x.
By solving both cases, we find the possible solutions to be x = 1 and x = -7.