Find the inverse function of f(x)= square root of 2x+2

The inverse function of the above function is f(x) =

You can find the inverse of any function by switching the f(x) and x terms. Once you have done that, solve for the new f(x). Finally, what you'll have remaining is the inverse function. The work is done for you below:

f(x) = ----> Switch the x and f(x)

x = ---> square both sides

= 2f(x) + 2 ---> subtract 2 from both sides

- 2 = 2f(x) ----> divide both sides by 2

= f(x) ----> switch the order for formatting sake.

f(x) =

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step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt