# Inverse function Values

Please solve each problem with a detailed solution showing each step to solve the problem. Since the symbols confuse me at times please use "baby" math to show how to get from the start to the end. I understand the book in some ways, but the more I see completed the better I can think about the rest of the problems I need to do. Also, if you type it all back to me, not a scanned print of your help, please keep things separated and neat please. Also, I am a returning adult student - you may know this stuff inside and out, but I do not. Thanks!

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Inverse function problems:

For the following problems a function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one to one.

1) X = 1, 2, 3, 4, 5, 6

F(x) = 1.5, 2.0, 3.6, 5.3, 2.8, 2.0

2) f(x) = ½(x+5)

3) g(x) = SQRT(x)

4) f(x) = 1+4x-x^2

5) h(x) = x^4+5

6) h(x) = x^4+5, 0 is <= x is <= 2

7) Please define a function and what is, what is its purpose in math? I know you say have f(2), well, you plug in 2 for x and solve and y is or ='s f(x), but what is the difference between x and f(x)?

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19) If f is a one to one function such that f(2) = 9, what is f^-1(9)?

20) If f(x) = x+cosx, find f^-1(1)

21) if h(x) = x + SQRT(x) find h^-1(6)

22) The formula C=(5/9)(F-32), where F is >= -459.67, expresses the Celsius temp. C as a function of the Fahrenheit temp F. Find a formula of the inverse function and interpret it. What is the domain of the inverse function?

23) Find a formula for the inverse functions.

a) f(x)=3-2x

b) f(x) = SQRT(10-3x)

c) y= (1-SQRT(x))/ (1+SQRT(x))

d) y = 2x^3 + 3

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35) For the next 3 problems show that

a) f is one to one.

b) Use theorem 7 to find g'(a), where g = f^-1.

c) Calculate g(x) and state the domain and range of g.

d) Calculate g'(a) from the formula in part c and check that it agrees with the result of part b.

e) Sketch the graphs of f and g on the same axes.

1) f(x) = x^3, a=8

2) f(x) = SQRT(x-2), a=2

3) f(x) =9-x^2, 0<= x<=3, a=8

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39) Find (f^-1)'(a)

F(x) =x^3+x+1

39) Find (f^-1)'(a)

F(x) =3+ x^2 + tan(pi(x)/2), -1<x<1, a=3

40) Suppose g is the inverse function of f and f(4) = 5, f'(4)=(2/3), find g'(5).

#### Solution Preview

Please see the attached file.

For the following problems a function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one to one.

1) X = 1, 2, 3, 4, 5, 6

F(x) = 1.5, 2.0, 3.6, 5.3, 2.8, 2.0

Ans: This function is one-one because for each x there exist exactly one f(x) and vice versa.

2) f(x) = ½(x+5)

Ans: This function is one-one because for each x there exist exactly one f(x) and vice versa. More precisely, the function is increasing function and if x1<=x2 then f(x1)<=f(x2)

3) g(x) = SQRT(x)

Ans: This function is NOT one-one because for example sqrt(4)=+2 or -2 which means for eaxh positive x we have 2 y,namely one positive and one negative.

4) f(x) = 1+4x-x^2

Ans: This function is NOT one-one because for example are two roots of this function which will yield zero for f(x) , Therefore it is not the same with definition of one-one which says "for each x one y and for each y one x"

5) h(x) = x^4+5

Ans: This function is NOT one-one because for example x=2 and x=-2 will give us f(x)=21

6) h(x) = x^4+5, 0 is <= x is <= 2

Ans: This function is one-one because the ...

#### Solution Summary

Inverse function values are computed. The formulas and verbal descriptions are determined.