BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2.7, Problem 76E
To determine

To find: The domain in which the given function becomes one-to-one and find the inverse of the function with the restricted domain.

Expert Solution

Answer to Problem 76E

The domain in which the given function is one-to-one is [1,] and the inverse of the function is g1(x)=x+1 and domain is [0,] .

Explanation of Solution

Given information:

  g(x)=(x1)2

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.7, Problem 76E

Concept used: A function with domain A is called a one-to-one function if no two elements of A have the same image, i.e.

  f(x1)f(x2)    Whenever x1x2

If f be a one-to-one function with domain A and range B. Then its inverse function f1 has domain B and range A and is defined by

  f1(y)=x      f(x)=y

Calculation:

From the given graph of the function, it is clear that the value of g(x) don’t repeat on the right hand side of x=1 . So, in the domain [1,] the given function is one-to-one.

  g(x)=(x1)2      1xy=(x1)2             0y(x1)=±yx=y+1               [ Ignore (-ve) value as 1x]g1(y)=y+1      0y

Therefore, the inverse of the given function with restricted domain can be written as

  g1(x)=x+1      [0,]

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