Suppose that the given function f is differentiable, has an inverse and that f (

Question

Suppose that the given function f is differentiable, has an inverse and that f(4) = -198. Find (f  -1) ' (-198).

f(x)= -3x^3-6

A. -144

B. -1/144

C. -288

D. -1/72

E. 1/144

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Suppose that the given function f is differentiable, has an inverse and that f(??2) = 4?. Find (f  -1) ' ( 4? ).

f(x)= 8x+4 cos(x)

A. -1/4

B. 1/2

C. -1/2

D.1/4

E.1/8

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A certain species of virulent bacteria is being grown in a culture. It is observed that the rate of growth of the bacterial population is proportional to the number present. If there were 3000 bacteria in the initial polulation and the number doubled after the first 60 minutes, how many bacteria will be present after 2 hours?

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Cobalt-60 is used extensively in medical technology. It has a half-life of 5.3 years. If you have 400 grams of cobalt now, how much was there 4 years ago?

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Find the area of the region bounded by the graph of f (x) and the x-axis from x = 0 to x = ln(3).

Explanation / Answer

1) we can find the inverse of the function with the following steps:

    write f(x) as y

    exchange places of x and y

    solve for y

    now write y as f inverse(x)

    the inverse of f(x) which i found out was =cuberoot(-(x+6)/3)

   put the value of x and find the answer

3) N=No x e^(-kt)

     6000 = 3000 * e^(-k)

     k = -0.693

     thus , after 2 hours N = 11996.47

4) k = ln(2)/half life

thus k = ln(2)/5.3

   N = No x e^(-kt)

N = 400 gms

thus No = 674.92gms

5) sinhx = (e^x + e^-x)/2

   thus solving we get answer as -2

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