What is \( (f-g)(x) \) ? \[ f(x)=x \] \( g(x)=3 x^{2}+9 x \) Write your answer as a polynomial or a rational function in simplest form. Save answer

To find \( (f - g)(x) \), subtract the function \( g(x) \) from \( f(x) \): \[ (f - g)(x) = f(x) - g(x) \] Given: \[ f(x) = x \] \[ g(x) = 3x^2 + 9x \] Substitute these into the equation: \[ (f - g)(x) = x - (3x^2 + 9x) \] Distribute the negative sign: \[ (f - g)(x) = x - 3x^2 - 9x \] Combine like terms: \[ (f - g)(x) = -3x^2 + (1x - 9x) \] \[ (f - g)(x) = -3x^2 - 8x \] **Final Answer:** \[ (f - g)(x) = -3x^{2} - 8x \]