Question

Consider the function f(x) = 5x + 7. Which statement MUST be true? A) f(1) ? f(3) = f(3) ? f(1) B) f(1) ? f(3) = f(5) ? f(3) C) f(1) ? f(3) = f(3) ? f(5) D) f(1) ? f(3) = f(?1) ? f(?3)

Answer 1

The answers are as follows for the functions.

f(1) = 12

f(3) = 22

f(5) = 32

Explanation:

To find any of these, simply input the value in for x in the equation given.

f(1)

f(x) = 5x + 7

f(x) = 5(1) + 7

f(x) = 5 + 7

f(x) = 12

You can repeat this for each of them and it will allow you to use all of the numbers in the equations given.

Answer 2

Option C is correct

`f(1)-f(3) =f(3)-f(5)`

Explanation:

Consider the function:

`f(x) =5x+7`

At x = 1

`f(1) =5(1)+7=5+7=12`

⇒f(1) = 12

At x = 3

`f(3) =5(3)+7=15+7=22`

⇒f(3) = 22

At x = 5

`f(5) =5( 5)+7=25+7=32`

⇒f(5) = 32

At x = -1

`f(-1) =5(-1)+7=-5+7=2`

⇒f(-1) = 2

At x = -3

`f(-3) =5(-3)+7=-15+7=-8`

⇒f(-3) = -8

A.

`f(1)-f(3) =f(3)-f(1)`

⇒
`12-22 = 22-12`

⇒
`-10= 10`

Option A is incorrect.

B.

`f(1)-f(3) =f(5)-f(3)`

⇒
`12-22 = 32-22`

⇒
`-10= 10`

Option B is incorrect.

C.

`f(1)-f(3) =f(3)-f(5)`

⇒
`12-22 = 22-32`

⇒
`-10= -10`

Option C is Correct.

D.

`f(1)-f(3) =f(-1)-f(-3)`

⇒
`12-22 = 2-(-8)`

⇒
`-10= 10`

Option D is incorrect.