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 2.1, Problem 21E
To determine

To evaluate g(x)=1x1+x at a number, we substitute the number for x in the definition of f(x) .

Expert Solution

Answer to Problem 21E

The values of the given functionare:

  g(2)=13,g(2)=3,g(12)=13,g(a)=1a1+a,g(a1)=2aa,g(1)=20(undefined)

Explanation of Solution

Given information: consider the function g(x)=1x1+x

Calculation:

Evaluate the values of the function g(x)=1x1+x for the given values of the variable x

Plug the value x=2, in the function g(x)=1x1+x then we get the value of g(2).

  g(2)=121+2g(2)=13

Plug the value x=2, in the function g(x)=1x1+x then we get the value of g(2).

  g(2)=1(2)1+(2)g(2)=1+212g(2)=31

Plug the value x=12, in the function g(x)=1x1+x then we get the value of g(12).

  g(12)=1(12)1+(12)g(12)=1232g(12)=13

Plug the value x=a in the function g(x)=1x1+x then we get the value of g(a).

  g(a)=1a1+a

Plug the value x=a1, in the function g(x)=1x1+x then we get the value of g(a1).

  g(a1)=1(a1)1+a1g(a1)=1a+11+a1g(a1)=2aa

Plug the value x=1, in the function g(x)=1x1+x then we get the value of g(1).

  g(1)=1(1)1+(1)g(1)=1+111g(1)=20

Thus, the values of the given functionare:

  g(2)=13,g(2)=3,g(12)=13,g(a)=1a1+a,g(a1)=2aa,g(1)=20(undefined)

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