a) To solve the equation f(x) = 6, we need to substitute the expression for f(x) into the equation and solve for x.
Given that f(x) = x - x, we can rewrite the equation as x - x = 6.
Simplifying, we have 0 = 6.
Since there is no value of x that satisfies this equation, there is no solution for f(x) = 6.
b) To solve the equation f(x) = g(x), we need to substitute the expressions for f(x) and g(x) into the equation and solve for x.
Given that f(x) = x - x and g(x) = x² - 3x - 12, we can rewrite the equation as x - x = x² - 3x - 12.
Simplifying, we have 0 = x² - 3x - 12.
To solve this quadratic equation, we can factor it or use the quadratic formula. Factoring, we get (x - 4)(x + 3) = 0.
Setting each factor equal to zero, we have x - 4 = 0 and x + 3 = 0.
Solving these equations, we find x = 4 and x = -3.
Therefore, the solutions to the equation f(x) = g(x) are x = 4 and x = -3.