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

Answer:

The answers are as follows for the functions.

f(1) = 12

f(3) = 22

f(5) = 32

Step-by-step 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

Answer:

Option C is correct

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

Step-by-step 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.