Answer:
The inverse of f(x) is
(x) = ±
+
Step-by-step explanation:
To find the inverse of the quadratic function f(x) = ax² + bx + c, you should put it in the vertex form f(x) = a(x - h)² + k, where
- h =
∵ f(x) = 3x² - 3x - 2
→ Compare it with the 1st form above to find a and b
∴ a = 3 and b = -3
→ Use the rule of h to find it
∵ h =
=
= 
∴ h = 
→ Substitute x by the value of h in f to find k
∵ k = 3(
)² - 3(
) - 2
∴ k = 
→ Substitute the values of a, h, and k in the vertex form above
∵ f(x) = 3(x -
)² + 
∴ f(x) = 3(x -
)² - 
Now let us find the inverse of f(x)
∵ f(x) = y
∴ y = 3(x -
)² - 
→ Switch x and y
∵ x = 3(y -
)² - 
→ Add
to both sides
∴ x +
= 3(y -
)²
→ Divide both sides by 3
∵
= (y -
)²
→ Take √ for both sides
∴ ±
= y - 
→ Add
to both sides
∴ ±
+
= y
→ Replace y by
(x)
∴
(x) = ±
+
∴ The inverse of f(x) is
(x) = ±
+
Statements Reasons
1. Write all the given as you did 1. Given
2. <DBA and <DBC are right angles 2. Def of perpendicular lines
3. m<DBA = 90 3. Def of right angle
m<DBC = 90
4. m<DBA = m<DBC 4. Substitution
5. m<DBA = m<1 + m<3 5. Angle addition postulate
m<DBC = m<2 + m<4
6. m<1 + m<3 = m<2 + m<4 6. Substitution
7. m<3 = m<4 7. Subtraction prop of equality
Answer:
could be either b or d
Step-by-step explanation:
<em>Answer:</em>
<em>80 books = $400</em>
<em>Step-by-step explanation:</em>
<em />
As the ratio 0.050:1 for Adalynn and the ratio 0.067:1 for Dwight are not equivalent, it shows that this is not a proportional relationship.
What is a proportional relationship?
Proportional relationships can be described as relationships between two variables that have equivalent ratios.
The ratio of Adalynn that planted 20 peach trees over 400 feet can be expressed as follows:
20:400
Divide through by 400, we have:
0.050:1
The ratio of Dwight that planted 18 plum trees over 270 feet can be expressed as follows:
Divide through by 270, we have:
0.067:1
Since the ratio 0.050:1 for Adalynn and the ratio 0.067:1 for Dwight are not equivalent, this implies that this is not a proportional relationship.
Learn more about the proportional relationship here: brainly.com/question/12917806.
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