Question

If x is an even number, the function f(x) = 2x − 1 gives an odd number. Identify the set of odd numbers corresponding to this set of even numbers: {0, 2, 4, 6, 8}. A. {3, 5, 7, 9, 11} B. {-1, 3, 7, 11, 15} C. {1, 3, 5, 9, 11} D. {5, 7, 9, 11, 13}

Answer 1

B. {-1, 3, 7, 11, 15}

Explanation:

In order to find the set of corresponding odd numbers then we have to put the even numbers one by one as we already know that x can only have even values..

So,

Putting x = 0

2(0) - 1

=0-1

= -1

Putting x=2

2(2) - 1

=4-1

=3

Putting x=4

2(4)-1

=8-1

=7

Putting x= 6

2(6) -1

=12-1

=11

Putting x=8

2(8)-1

=16-1

=15

So the corresponding set for {0, 2, 4, 6, 8} is {-1, 3, 7, 11, 15}

Hence, option B is the correct answer ..

Answer 2

B. {-1, 3, 7, 11, 15}

Explanation:

The given function is
`f(x)=2x-1`

To find the corresponding odd numbers, we substitute the even numbers as x-values into the function.

When x=0,
`f(0)=2(0)-1=-1`

When x=2,
`f(2)=2(2)-1=3`

When x=4,
`f(4)=2(4)-1=7`

When x=6,
`f(6)=2(6)-1=11`

When x=8,
`f(8)=2(8)-1=15`

Therefore the set of odd numbers corresponding to this set of even numbers are {-1, 3, 7, 11, 15}