f(x)=3x-1, g(x)= x^2-6x+16 (f*g)(x)=23
I do not know where to begin. Please help
To find the value of (f*g)(x), you need to find the product of f(x) and g(x), and then set it equal to 23. Let's break it down step by step:
1. Start with the given functions:
f(x) = 3x - 1
g(x) = x^2 - 6x + 16
2. To find (f*g)(x), you need to multiply f(x) and g(x):
(f*g)(x) = f(x) * g(x)
3. Substitute the functions:
(f*g)(x) = (3x - 1) * (x^2 - 6x + 16)
4. Simplify the expression by multiplying the terms:
(f*g)(x) = 3x * x^2 - 3x * 6x + 3x * 16 - 1 * x^2 + 1 * 6x - 1 * 16
(f*g)(x) = 3x^3 - 18x^2 + 48x - x^2 + 6x - 16
5. Combine like terms:
(f*g)(x) = 3x^3 - x^2 - 12x - 16
6. Now, set the expression equal to 23 and solve for x:
3x^3 - x^2 - 12x - 16 = 23
This is a cubic equation, so it might not have a simple solution. To solve it, you can use numerical methods like graphing or iterative approximation. Alternatively, you may use software or calculators capable of solving equations.
Keep in mind that the solution you find for x will be the x-value(s) where the function (f*g)(x) equals 23.