Hey there! Did you know that mathematics can unlock the secrets to freedom? Well, it’s true! In this problem, we’ll explore the functions F(X) = 16x – 30 and G(X) = 14x – 6.

These functions represent different paths, each with its own unique equation. Now, imagine the magic that happens when we combine them by subtracting G(X) from F(X) to get (F – G)(X).

The question is, at which value of X does this combined function equal zero? By solving this equation, we’ll find the point where these paths intersect and freedom is achieved.

So, let’s dive in and discover the value of X that leads us to the land of equilibrium!

## Understanding the Functions F(X) and G(X)

To understand the functions F(X) and G(X), you need to know their equations and what they represent.

Comparing the slopes of f(x) and g(x) will reveal their rates of change.

The x-intercept of the (f – g)(x) graph can be found by setting the equation equal to zero and solving for x.

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## Evaluating (F – G)(X) and Setting It to Zero

Evaluating the difference between F(X) and G(X) by subtracting G(X) from F(X) will allow you to determine the value of X for which (F – G)(X) equals zero.

To evaluate (F – G)(X), simply substitute the expressions for F(X) and G(X) into the equation and simplify.

By setting the resulting expression equal to zero, you can solve for X.

This process involves analyzing the relationship between F(X) and G(X) and finding the specific value of X that makes their difference equal to zero.

## Solving the Equation (F – G)(X) = 0 for X

To solve the equation (F – G)(X) = 0 for X, you need to find the value of X that makes the difference between F(X) and G(X) equal to zero. In this case, (F – G)(X) = 0 means that F(X) = G(X).

By setting 16x – 30 equal to 14x – 6, you can find the value of X that satisfies the equation.

## Interpreting the Intersection of F and G

When finding the intersection of F(X) = 16x – 30 and G(X) = 14x – 6, you can determine the value of X that satisfies the equation (F – G)(X) = 0.

The intersection of F and G occurs when the two functions have the same value.

To analyze the graphical representation of f(x) and g(x) at their intersection, you can plot both equations on a graph and find the point where they intersect.

Exploring the real-life applications of finding the value of x when (f – g)(x) = 0 can help in various scenarios, such as identifying the break-even point in business or determining the equilibrium point in economics.

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## Conclusion

In conclusion, solving the equation (f – g)(x) = 0 for x requires careful evaluation and interpretation. By setting (f – g)(x) to zero, we can find the value of x where the two functions intersect.

So, after applying logical and concise steps, we can determine that the value of x, where (f – g)(x) equals zero, is 2.

This intersection point provides insight into the relationship between f(x) and g(x) and allows for further analysis of their behavior.