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Sagot :
The inverse of the function for square feet, gives the area in square yard
from which the cost of the flooring is calculated as $539.7.
Response:
a. The inverse [tex]\underline{f^{-1}(x) = \dfrac{x}{9}}[/tex] can be used by the Clearys to calculate the cost if the flooring.
b. $539.7
What is the inverse of a function and how can it be used?
Given:
The dimensions of the flooring = 15 foot by 18 foot
Cost of the new flooring = $17.99/yd.²
The formula that converts square yards to square feet is f(x) ≈ 9·x
a. The inverse function gives the x-values as an output from an input of
the y-value.
The inverse of the function, f⁻¹(x), is the function that converts square
feet to square yards, which is given as follows;
- [tex]\underline{f^{-1}(x) = \dfrac{x}{9}}[/tex]
The significance of f⁻¹(x) for the Clearys is that it gives the number of
square yards required for the flooring from the square feet, from which
the cost of the flooring can be calculated.
b. The cost of the new flooring is therefore;
[tex]Cost = \$17.99/yd.^2 \times f^{-1}(x) = \$17.99/yd.^2 \times \dfrac{15 \, ft. \times 18 \, ft. }{9} = \mathbf{\$539.7}[/tex]
- The new flooring will cost $539.7
Learn more about inverse functions here:
https://brainly.com/question/2873333
https://brainly.com/question/1540214
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