YouLet f(x) = - x ^ 2 - 5 and g(x) = 3x + 2Find and simplify (g f) (x) .A. (g f) (x) = 9x ^ 2 + 12x - 1B. (g f) (x) = - 3x ^ 2 - 13C. (g f) (x) = - 3x ^ 3 - 15x + 2D. (q f) (x) = - 9x ^ 2 - 12x - 9

The function (g f)(x) is the composition of the functions g and f, which means that you apply the function f first and then apply the function g to the result.

Here are the steps to find (g f)(x):

1. Start with the function f(x) = -x^2 - 5.
2. Then apply the function g to f(x). This means that wherever there is an x in the function g, you replace it with the function f. So g(f(x)) = 3f(x) + 2.
3. Substitute f(x) = -x^2 - 5 into the equation from step 2 to get g(f(x)) = 3(-x^2 - 5) + 2.
4. Simplify the equation to get g(f(x)) = -3x^2 - 15 + 2.
5. Simplify further to get g(f(x)) = -3x^2 - 13.

So, the correct answer is B. (g f) (x) = - 3x ^ 2 - 13.