9514 1404 393
Answer:
f^-1(x) = 4+∛((x-6)/5)
Step-by-step explanation:
To find the inverse function, solve ...
x = f(y)
then write the answer in functional form.
![\displaystyle x=f(y)\\\\x=5(y-4)^3+6\\\\x-6=5(y-4)^3\\\\\frac{x-6}{5}=(y-4)^3\\\\\sqrt[3]{\frac{x-6}{5}}=y-4\\\\y=4+\sqrt[3]{\frac{x-6}{5}}\\\\\boxed{f^{-1}(x)=4+\sqrt[3]{\frac{x-6}{5}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3Df%28y%29%5C%5C%5C%5Cx%3D5%28y-4%29%5E3%2B6%5C%5C%5C%5Cx-6%3D5%28y-4%29%5E3%5C%5C%5C%5C%5Cfrac%7Bx-6%7D%7B5%7D%3D%28y-4%29%5E3%5C%5C%5C%5C%5Csqrt%5B3%5D%7B%5Cfrac%7Bx-6%7D%7B5%7D%7D%3Dy-4%5C%5C%5C%5Cy%3D4%2B%5Csqrt%5B3%5D%7B%5Cfrac%7Bx-6%7D%7B5%7D%7D%5C%5C%5C%5C%5Cboxed%7Bf%5E%7B-1%7D%28x%29%3D4%2B%5Csqrt%5B3%5D%7B%5Cfrac%7Bx-6%7D%7B5%7D%7D%7D)
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The graph shows the function and its inverse to be reflections of each other in the line y=x, as they should be.
Answer:
20 days
Step-by-step explanation:
It takes 12 men 5 days to complete a job. Work out how many days it would take 3 men to complete the same job.
12 * 5 = 60
60/3 = 20
It will take 3 men 20 days to do the same job
Answer:
9
Step-by-step explanation:
Let the two perfect cubes be x and y where x > y.
According to the given conditions:
![{x}^{3} - {y}^{3} = 386...(1) \\ y = 7...(2) \\ plug \: y = 7 \: in \: equation \: (1) \\ {x}^{3} - {7}^{3} = 386 \\ {x}^{3} - 343 = 386 \\ {x}^{3} = 343 + 386 \\ {x}^{3} = 343 + 386 \\ {x}^{3} = 729 \\ x = \sqrt[3]{729} \\ x = 9](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B3%7D%20%20-%20%20%7By%7D%5E%7B3%7D%20%20%3D%20386...%281%29%20%5C%5C%20y%20%3D%207...%282%29%20%5C%5C%20plug%20%5C%3A%20y%20%3D%207%20%5C%3A%20in%20%5C%3A%20equation%20%5C%3A%20%281%29%20%5C%5C%20%20%7Bx%7D%5E%7B3%7D%20%20-%20%20%7B7%7D%5E%7B3%7D%20%20%3D%20386%20%5C%5C%20%7Bx%7D%5E%7B3%7D%20%20-%20%20343%20%3D%20386%20%5C%5C%20%7Bx%7D%5E%7B3%7D%20%20%20%20%20%3D%20343%20%20%2B%20%20386%20%5C%5C%20%7Bx%7D%5E%7B3%7D%20%20%20%20%20%3D%20343%20%20%2B%20%20386%20%5C%5C%20%7Bx%7D%5E%7B3%7D%20%20%20%3D%20729%20%5C%5C%20x%20%3D%20%20%5Csqrt%5B3%5D%7B729%7D%20%20%5C%5C%20x%20%3D%209)
Thus the cube root of the larger number is 9.
Answer:
103 and 102
Step-by-step explanation:
u add them together
Answer:
<h2>$66</h2>
Step-by-step explanation:
Step one:
given data
charges
$4 per bag
$10 weekly fee
let the number of bag be x
and let the total charges be y
<em>the linear function for the total per week is</em>
<em>y=4x+10</em>
Step two:
the independent variable is the weekly fee of $10
for x=14
y=4(14)+10
y=56+10
y=$66
