Question

Solve the system of equations. Type in all points of intersection for the two functions and round to the nearest tenth if necessary? f(x) = √5x+25-1 g(x) = x2 - 2x - 3 2

Answer 1

To solve the system of equations f(x) = sqrt(5x+25)-1 and g(x) = x^2-2x-3, follow these steps: rewrite f(x) with the radical as a power, substitute f(x) into g(x), solve for x, and round the points of intersection if necessary.

Step-by-step explanation:

To solve the system of equations f(x) = sqrt(5x+25)-1 and g(x) = x^2-2x-3, we need to find the points of intersection. Let's solve them step by step.

1. First, let's rewrite the equation f(x) with the radical as a power: f(x) = (5x+25)^(1/2) - 1.
2. Next, we'll substitute the value of f(x) into g(x): (5x+25)^(1/2) - 1 = x^2 - 2x - 3.
3. To solve for x, we'll move all terms to one side of the equation and use a calculator or computer to simplify and solve for x.
4. The points of intersection are the x-values we obtained in the previous step. Round them to the nearest tenth if necessary.

By following these steps, you will find the points of intersection between the two functions f(x) and g(x).