9514 1404 393
Answer:
1) f⁻¹(x) = 6 ± 2√(x -1)
3) y = (x +4)² -2
5) y = (x -4)³ -4
Step-by-step explanation:
In general, swap x and y, then solve for y. Quadratics, as in the first problem, do not have an inverse function: the inverse relation is double-valued, unless the domain is restricted. Here, we're just going to consider these to be "solve for ..." problems, without too much concern for domain or range.
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1) x = f(y)
x = (1/4)(y -6)² +1
4(x -1) = (y-6)² . . . . . . subtract 1, multiply by 4
±2√(x -1) = y -6 . . . . square root
y = 6 ± 2√(x -1) . . . . inverse relation
f⁻¹(x) = 6 ± 2√(x -1) . . . . in functional form
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3) x = √(y +2) -4
x +4 = √(y +2) . . . . add 4
(x +4)² = y +2 . . . . square both sides
y = (x +4)² -2 . . . . . subtract 2
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5) x = ∛(y +4) +4
x -4 = ∛(y +4) . . . . . subtract 4
(x -4)³ = y +4 . . . . . cube both sides
y = (x -4)³ -4 . . . . . . subtract 4
Answer:
a) Yes.
Step-by-step explanation:
A function does not have any repeating values for a given x-value. According to the values of the table, there aren't multiple y-values for a given x-value. Therefore, the table represents a function.
Answer: 41.58$
Step-by-step explanation:
The difference between Pre-Image and Image is given as follows:
- Image is the shape AFTER a transformation is the picture of the transformation.
- A transformation's preimage is the shape BEFORE the change.
<h3>How do you define relationships between Image and Preimage?</h3>
Usually, the difference between image and pre-image is the way or method of transformation.
<h3>What is transformation in math?</h3>
A transformation is a broad phrase covering four distinct methods of changing the shape and/or location of a point, line, or geometric figure.
The Pre-Image is the original shape of the item, and the Image during the transformation is the final shape and location of the object.
The types of transformation in math are;
- translation
- rotation
- reflection, and
- dilation.
Learn more about pre-image:
brainly.com/question/8405245
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