Question

The function below is defined by two equations. The equation in the first row gives the output for negative numbers in the domain. The equation in the second row gives the output for​ non-negative numbers in the domain. Find the indicated function values.

f (x) = { 5x+7 if x < 0

{ 7x+8 if x ≥ 0

(a) f (- 4)
(b) f (2)
(c) f (0)
(d) f (-100) + f(100)
(e) f (- 4) = ____ (Simplify your answer.)
(f) f (2) = ____ (Simplify your answer.)
(g) f (0) = ____ (Simplify your answer.)
(h) f (-100) + f(100) = ____ (Simplify your answer.)

Answer 1

Explanation:

In order to know which equation we need to consider, we have to check the value of x. If x is negative, we will replace x in the first equation and if x is positive or null we will replace it in the second equation.

(a) x=-4 so x is negative. We use the first equation
`f(x)=5x+7` and we have
`f(-4)=5*(-4)+7=-13`

(b)x=2 and is positive so we use the second equation
`f(x)=7x+8`. The result is
`f(2)=7*(2)+8=22`

(c)x=0 In this case the function is defined by the second equation
`f(x)=7x+8`. So
`f(0)=7*(0)+8=8`

(d)Here we have both case in the same calcul. We need to calculate the fonction values of each one and then make the sum.

With
`f(-100)`, x=-100 and is negative so we use the first equation
`f(x)=5x+7` and we have
`f(-100)=5*(-100)+7=-493`.

With
`f(00)`, x=100 ans is positive so we use the second equation
`f(x)=7x+8` and get
`f(100)=7*100+8=708`.

We add them to get the result :
`f(-100)+f(100)=-493+708=215`

(e)
`f(-4)=-13`

(f)
`f2)=22`

(g)
`f(0)=8`

(h)
`f(-100)+f(100)=215`