1) Which of the given functions is a one-to-one function? Select all that apply
g(x)=2sqrt(x+5)
g(x)=5x^2-2
h(x)=x^4+5
f(x)=Abs(x)
f(x)=-5x+2

2) Which of the given functions is a one-to-one function? Select all that apply
g(x)=3sqrt(x)
f(x)=-2x+3
g(x)=2x^2-3x
f(x)=1/x
h(x)=x^4+5

3) Assume that f is a one to one function
A) If f(-2)=2, find f^-1(2)
B)If f^-1(6)=-4, find f(-4).

4)A tank holds 100 gallons of water, which drains from a leak at the bottom, causing the tank to empty in 44 minutes. Toricelli's Law gives the volume of water remaining in the tank after t minutes as follows.
V(t)=100(1-t/44)^2
A) find V^-1
b) find V^-1(18). Round your answer to the nearest tenths place.

5)For his services, a private investigator requires a $600 retention fee plus $105 per hour. Let x represent the number of hours the investigator spends working on a case.

(a) Find a function f that models the investigator's fee as a function of x.
(b) Find f -1(x).
(c) Find f -1(1650).

Solution Preview

1) Which of the given functions is a one-to-one function? Select all that apply.
g(x)=2sqrt(x+5) : is NOT one to one because it is not a surjection.
g(x)=5x^2-2 : is NOT one to one because if g(x1)=g(x2) => 5(x1)^2-2=5(x2)^2-2 => (x1)^2=(x2)^2 => x1=plus-minus x2 and it is not an injection.
h(x)=x^4+5 : is NOT one to one because if h(x1)=h(x2) => (x1)^4=(x2)^4 => x1=plus-minus x2 and it is not an injection.
f(x)=Abs(x) : is NOT one to one because if f(x1)=f(x2) => ...

... Discrete Functions are scrutinized. ... 2 / 2 . By the definition above, we know that g is not a 1-1 (one-to-one) function. ... 1 f is the inverse function of f ...

... to determine (no proof necessary) whether f is a one-to-one function. ... c. Let g be the function g: R → R defined ... your solution, g-1 is really the inverse of g ...

... Suppose that is a one-to-one function. ... (v) Group Code An encoding function is called ... in , (b) If and belongs to , then , (c) If is in , then its inverse is in ...

... Find the inverse of the one-to-one function. f(x) = (x - 5)3. A) f-1(x) = -5. B) f-1(x) = +5. C) f-1(x) = + 125. D) f-1(x) = +5 1. Given functions f and g, perform ...

... Use the distributive laws. 4. Determine whether each of these functions from Z to Z is one-to-one. Explain. ... 4. (a) A function is called "one-to-one" when. ...

... g(1/2) = 1. Now, choose n=2. g(2/2)=g(1)=1. Since g(1/2) = g(2/2), g is not a one-to-one function. (c) To find the inverse of f ...One-to-one functions are examined ...

... keep in mind that a function is a one-to-one map from ... that it is also possible to reflect functions on a ... although in these cases the resulting function is not ...

... This implies that is one-to-one. ... So has an inverse and its inverse is also an isomorphism. ... The expert examines schur's lemma implying functions. ...

... a-1aba =a-1aab inverses and left side associative property. ... To show the function is an automorphism we show: 1. that Ø (a,b) = (b,a) is one to one: Ø (a1, b1 ...