Please help me solve and find the excluded values for this problem. Also please show me the work for this problem I want to learn!F(h) = x^2-9/x^2-4x+3
division by zero is not defined. So, when the denominator is zero, f(x) is not defined.
x^2-4x+3 = (x-1)(x-3)
so, when x=1 or 3, you are trying to divide by zero. Those values are not part of the domain.
Note that x^2-9 = (x-3)(x+3)
So, for any value except x=3, f(x) = (x+3)/(x-1)
The graph available below should help you explore other properties of f(x).
http://www.wolframalpha.com/input/?i=%28x^2-9%29%2F%28x^2-4x%2B3%29
To solve the problem and find the excluded values, we need to determine the values of x that would make the expression undefined. This happens when there is a division by zero.
Given function:
F(h) = (x^2 - 9) / (x^2 - 4x + 3)
To find the excluded values, we need to identify the values of x that will make the denominator of the fraction equal to zero. This is because division by zero is undefined.
Step 1: Set the denominator equal to zero and solve for x.
x^2 - 4x + 3 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula.
Method 1: Factoring
The equation factors into:
(x - 1)(x - 3) = 0
Now, set each factor equal to zero:
x - 1 = 0 and x - 3 = 0
Solving these equations, we find:
x = 1 and x = 3
Method 2: Quadratic Formula
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the quadratic equation x^2 - 4x + 3 = 0:
a = 1, b = -4, and c = 3
Plugging these values into the formula, we get:
x = (-(-4) ± √((-4)^2 - 4(1)(3))) / (2(1))
Simplifying further:
x = (4 ± √(16 - 12)) / 2
x = (4 ± √4) / 2
x = (4 ± 2) / 2
Solving for x, we find:
x = 3 and x = 1
Step 2: Check the excluded values by substituting them back into the original function.
Now that we have found the values of x that make the denominator zero (excluded values), we should check if these values also make the function undefined by substituting them back into the original function.
For x = 1:
F(h) = (1^2 - 9) / (1^2 - 4(1) + 3)
= (-8) / (0)
The function is undefined when x = 1.
For x = 3:
F(h) = (3^2 - 9) / (3^2 - 4(3) + 3)
= (0) / (0)
The function is undefined when x = 3.
So, the excluded values for this function are x = 1 and x = 3.
To summarize:
The excluded values for the given function F(h) = (x^2 - 9) / (x^2 - 4x + 3) are x = 1 and x = 3.