To find : the domain of the function so that the function is one-to-one and has an inverse function. And find the inverse function.

Expert Solution & Answer

Answer to Problem 85E

The domain of function $f$ is $x≥−2$ for having one-to-one function and inverse function is $f−1(x)=x−2$ .

Explanation of Solution

Given information :

The function $f(x)=|x+2|$ .

Calculation : the domain of function is all real numbers. To having the function one-to-one and inverse, for every value of x , there should be unique value of y.

So the domain of function should be $x≥−2$ .

To find the inverse function substitute $f(x)=y$ in the function and simplify it,

$f(x)=|x+2|y=|x+2| [substitute f(x)=y]x+2=y [remove mod with positive sign for x≥−2]x=y−2 [subtract 2 from both side]f−1(x)=x−2 [simplify]$

Thus, the inverse function is $f−1(x)=x−2$ .

The domain of the function f is all real values because function is defined for all real values.

The range of the function f is $[0,∞)$ , the minimum value $0$ is occur at $x=−2$ .

The domain of function $f−1$ is the range of the function f.

Thus, the domain of the function $f−1$ is $[0,∞)$ .

For range of the function $f−1$ , the minimum value $−2$ is occur at $x=0$ ,

Thus, the range of the function $f−1$ is $[−2,∞)$ .

Chapter 1.6, Problem 84E

Chapter 1.6, Problem 86E

Chapter 1 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E

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Prob. 128E Ch. 1.6 - Prob. 129E Ch. 1.6 - Prob. 130E Ch. 1.6 - Prob. 131E Ch. 1.6 - Prob. 132E Ch. 1.6 - Prob. 133E Ch. 1.6 - Prob. 134E Ch. 1.6 - Prob. 135E Ch. 1.6 - Prob. 136E Ch. 1.6 - Prob. 137E Ch. 1.6 - Prob. 138E Ch. 1.6 - Prob. 139E Ch. 1.6 - Prob. 140E Ch. 1.6 - Prob. 141E Ch. 1.6 - Prob. 142E Ch. 1.6 - Prob. 143E Ch. 1.6 - Prob. 144E Ch. 1.7 - Prob. 1E Ch. 1.7 - Prob. 2E Ch. 1.7 - Prob. 3E Ch. 1.7 - Prob. 4E Ch. 1.7 - Prob. 5E Ch. 1.7 - Prob. 6E Ch. 1.7 - Prob. 7E Ch. 1.7 - Prob. 8E Ch. 1.7 - Prob. 9E Ch. 1.7 - Prob. 10E Ch. 1.7 - Prob. 11E Ch. 1.7 - Prob. 12E Ch. 1.7 - Prob. 13E Ch. 1.7 - Prob. 14E Ch. 1.7 - Prob. 15E Ch. 1.7 - Prob. 16E Ch. 1.7 - Prob. 17E Ch. 1.7 - Prob. 18E Ch. 1.7 - Prob. 19E Ch. 1.7 - Prob. 20E Ch. 1.7 - Prob. 21E Ch. 1.7 - Prob. 22E Ch. 1.7 - Prob. 23E Ch. 1.7 - Prob. 24E Ch. 1.7 - Prob. 25E Ch. 1.7 - Prob. 26E Ch. 1.7 - Prob. 27E Ch. 1.7 - Prob. 28E Ch. 1.7 - Prob. 29E Ch. 1.7 - Prob. 30E Ch. 1.7 - Prob. 31E Ch. 1.7 - Prob. 32E Ch. 1.7 - Prob. 33E Ch. 1.7 - Prob. 34E Ch. 1 - Prob. 1CR Ch. 1 - Prob. 2CR Ch. 1 - Prob. 3CR Ch. 1 - Prob. 4CR Ch. 1 - Prob. 5CR Ch. 1 - Prob. 6CR Ch. 1 - Prob. 7CR Ch. 1 - Prob. 8CR Ch. 1 - Prob. 9CR Ch. 1 - Prob. 10CR Ch. 1 - Prob. 11CR Ch. 1 - Prob. 12CR Ch. 1 - Prob. 13CR Ch. 1 - Prob. 14CR Ch. 1 - Prob. 15CR Ch. 1 - Prob. 16CR Ch. 1 - Prob. 17CR Ch. 1 - Prob. 18CR Ch. 1 - Prob. 19CR Ch. 1 - Prob. 20CR Ch. 1 - Prob. 21CR Ch. 1 - Prob. 22CR Ch. 1 - Prob. 23CR Ch. 1 - Prob. 24CR Ch. 1 - Prob. 25CR Ch. 1 - Prob. 26CR Ch. 1 - Prob. 27CR Ch. 1 - Prob. 28CR Ch. 1 - Prob. 29CR Ch. 1 - Prob. 30CR Ch. 1 - Prob. 31CR Ch. 1 - Prob. 32CR Ch. 1 - Prob. 33CR Ch. 1 - Prob. 34CR Ch. 1 - Prob. 35CR Ch. 1 - Prob. 36CR Ch. 1 - Prob. 37CR Ch. 1 - Prob. 38CR Ch. 1 - Prob. 39CR Ch. 1 - Prob. 40CR Ch. 1 - Prob. 41CR Ch. 1 - Prob. 42CR Ch. 1 - Prob. 43CR Ch. 1 - Prob. 44CR Ch. 1 - Prob. 45CR Ch. 1 - Prob. 46CR Ch. 1 - Prob. 47CR Ch. 1 - Prob. 48CR Ch. 1 - Prob. 49CR Ch. 1 - Prob. 50CR Ch. 1 - Prob. 51CR Ch. 1 - Prob. 52CR Ch. 1 - Prob. 53CR Ch. 1 - Prob. 54CR Ch. 1 - Prob. 55CR Ch. 1 - Prob. 56CR Ch. 1 - Prob. 57CR Ch. 1 - Prob. 58CR Ch. 1 - Prob. 59CR Ch. 1 - Prob. 60CR Ch. 1 - Prob. 61CR Ch. 1 - Prob. 62CR Ch. 1 - Prob. 63CR Ch. 1 - Prob. 64CR Ch. 1 - Prob. 65CR Ch. 1 - Prob. 66CR Ch. 1 - Prob. 67CR Ch. 1 - Prob. 68CR Ch. 1 - Prob. 69CR Ch. 1 - Prob. 70CR Ch. 1 - Prob. 71CR Ch. 1 - Prob. 72CR Ch. 1 - Prob. 73CR Ch. 1 - Prob. 74CR Ch. 1 - Prob. 75CR Ch. 1 - Prob. 76CR Ch. 1 - Prob. 77CR Ch. 1 - Prob. 78CR Ch. 1 - Prob. 79CR Ch. 1 - Prob. 80CR Ch. 1 - Prob. 81CR Ch. 1 - Prob. 82CR Ch. 1 - Prob. 83CR Ch. 1 - Prob. 84CR Ch. 1 - Prob. 85CR Ch. 1 - Prob. 86CR Ch. 1 - Prob. 87CR Ch. 1 - Prob. 88CR Ch. 1 - Prob. 89CR Ch. 1 - Prob. 90CR Ch. 1 - Prob. 91CR Ch. 1 - Prob. 92CR Ch. 1 - Prob. 93CR Ch. 1 - Prob. 94CR Ch. 1 - Prob. 95CR Ch. 1 - Prob. 96CR Ch. 1 - Prob. 97CR Ch. 1 - Prob. 98CR Ch. 1 - Prob. 99CR Ch. 1 - Prob. 100CR Ch. 1 - Prob. 101CR Ch. 1 - Prob. 102CR Ch. 1 - Prob. 103CR Ch. 1 - Prob. 104CR Ch. 1 - Prob. 105CR Ch. 1 - Prob. 106CR Ch. 1 - Prob. 107CR Ch. 1 - Prob. 108CR Ch. 1 - Prob. 109CR Ch. 1 - Prob. 110CR Ch. 1 - Prob. 1CT Ch. 1 - Prob. 2CT Ch. 1 - Prob. 3CT Ch. 1 - Prob. 4CT Ch. 1 - Prob. 5CT Ch. 1 - Prob. 6CT Ch. 1 - Prob. 7CT Ch. 1 - Prob. 8CT Ch. 1 - Prob. 9CT Ch. 1 - Prob. 10CT Ch. 1 - Prob. 11CT Ch. 1 - Prob. 12CT Ch. 1 - Prob. 13CT Ch. 1 - Prob. 14CT Ch. 1 - Prob. 15CT Ch. 1 - Prob. 16CT Ch. 1 - Prob. 17CT Ch. 1 - Prob. 18CT Ch. 1 - Prob. 19CT Ch. 1 - Prob. 20CT

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