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# One-To-One Functions and Inverses

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

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) => ...

#### Solution Summary

One-To-One Functions and Inverses are entailed.

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