The average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values.
Hi there!
![\large\boxed{f^{-1}(x) = \sqrt[3]{\frac{x+4}{9} } }](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7Bf%5E%7B-1%7D%28x%29%20%3D%20%20%5Csqrt%5B3%5D%7B%5Cfrac%7Bx%2B4%7D%7B9%7D%20%7D%20%7D)
Find the inverse by replacing f(x) with y and swapping the x and y variables:
Isolate y by adding 4 to both sides:
Divide both sides by 9:
Take the cube root of both sides:
![y = \sqrt[3]{\frac{x+4}{9} }\\\\f^{-1}(x) = \sqrt[3]{\frac{x+4}{9} }](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7Bx%2B4%7D%7B9%7D%20%7D%5C%5C%5C%5Cf%5E%7B-1%7D%28x%29%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7Bx%2B4%7D%7B9%7D%20%7D)
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1.
f(x) = x
g(x) = x + 3
For each x value you use in f(x) and g(x), the corresponding y value in g(x) is always 3 more than in f(x). If each y-coordinate is 3 more, that means the graph is shifted 3 units up. The graph of f(x) is shifted 3 units up to create the graph of g(x).
2.
The first term is -0.5.
Then each term goes up by 0.25.
1st term: -0.5
2nd term: -0.5 + 0.25 = -0.5 + 0.25(1)
3rd term: -0.5 + 0.25 + 0.25 = -0.5 + 0.25(2)
4th term: -0.5 + 0.25 + 0.25 + 0.25 = -0.5 + 0.25(3)
nth term: -0.5 + 0.25(n - 1)
-0.5 + 0.25(n - 1) = -0.5 + 0.25n - 0.25 = -0.75 + 0.25n = 0.25n - 0.75
Answer is C.
Answer:
50
Step-by-step explanation:
4,500÷90=50
and to check
90×50=4500
