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:
4 units squared and 6 units squared.
Hope this helps!
Answer:
22
Step-by-step explanation:
We can use the order of operations (PEMDAS), to solve this equation.
We must first multiply and divide, and order. This means we divide 12 by 3 and get 4, then multiply that by 2 and get 8. (30-12÷3×2,30-4×2,30-8). Now we just subtract 8 from 30 and get 22 as our answer.
Dave will have $12,728 after 15 years, if he has $8000 to invest for 15 years. He finds a bank that offers an interest rate of 3.1% compounded monthly.
Step-by-step explanation:
The given is,
Investment = $ 8000
No. of years = 15 years
Interest rate, i = 3.1 %
( compounded monthly )
Step:1
For for calculating future value with compound interest monthly,
.................(1)
Where,
A = Future amount
P = Initial investment
r = Rate of interest
n = Number of compounding in a year
t = Time period
Step:2
From given values,
P = $8000
r = 3.1%
t = 15 years
n = 12 ( for monthly)
Equation (1) becomes,





A = $ 12728.48
Result:
Dave will have $12,728 after 15 years, if he has $8000 to invest for 15 years. He finds a bank that offers an interest rate of 3.1% compounded monthly.
Answer:
(a) discriminant is positive, 76
(b) the above tells you there are two real roots
Step-by-step explanation:
the discriminant is 'b² - 4ac'
3x² - 2x - 6 = 0 ∴ a = 3, b = -2, c = -6
(-2)² - 4(3)(-6) = 4 + 72