The functions f(x)=x2−2x−4 and g(x)=45x−2 are shown on the coordinate plane below.
Select all answer choices that best represent solutions to the equation f(x)=g(x).
1. x=3.4x is equal to 3 point 4
2. x=−1.9x is equal to negative 1 point 9
3. x=−0.6x is equal to negative 0 point 6
4. x=2.5x is equal to 2 point 5
5. x=−1.2
To find the solutions to the equation f(x) = g(x), you need to set the two functions equal to each other and then solve for x.
f(x) = g(x)
x^2 - 2x - 4 = 45x - 2
To solve this equation, bring all terms to one side:
x^2 - 2x - 4 - 45x + 2 = 0
x^2 - 47x - 2 = 0
Now, you can solve this quadratic equation using factoring, completing the square, or using the quadratic formula. In this case, factoring or using the quadratic formula would be most appropriate.
Factoring: Unfortunately, this quadratic equation cannot be easily factored.
Quadratic formula: The quadratic formula can be used to solve any quadratic equation of the form ax^2 + bx + c = 0. The formula is as follows:
x = (-b ± √(b^2 - 4ac)) / 2a
For our equation, a = 1, b = -47, and c = -2. Plugging these values into the formula:
x = (-(-47) ± √((-47)^2 - 4(1)(-2))) / (2(1))
x = (47 ± √(2209 + 8)) / 2
x = (47 ± √(2217)) / 2
Now, you can simplify further by finding the square root of 2217:
x ≈ (47 ± 47.067) / 2
Simplifying further:
x ≈ (47 + 47.067) / 2 ≈ 94.067 / 2 ≈ 47.0335
x ≈ (47 - 47.067) / 2 ≈ -0.067 / 2 ≈ -0.0335
Therefore, the solutions to the equation f(x) = g(x) are approximately x = 47.0335 and x ≈ -0.0335.
Looking at the answer choices provided:
1. x = 3.4: This is not a solution to the equation f(x) = g(x).
2. x = -1.9: This is not a solution to the equation f(x) = g(x).
3. x = -0.6: This is not a solution to the equation f(x) = g(x).
4. x = 2.5: This is not a solution to the equation f(x) = g(x).
5. x = -1.2: This is not a solution to the equation f(x) = g(x).
None of the answer choices represent solutions to the equation f(x) = g(x).
x^2 - 2x - 4 = 45x - 2
x^2 - 47x - 2 = 0
x = (47±√2217)/2
since √2217 ≈ 47, you basically have
(47±47)/2 = 47 or 0
clearly you have a typo. I suspect you meant
x^2 - 2x - 4 = 4/5 x - 2
x^2 - 2.8x - 2 = 0
now solve that to get your answer.