Let

f(x) = ax + 3 if x > 0

f(x) = ab if x = 0

f(x) = bx + c if x < 0

If f(2) = 5, f(0) = 2, and f(-2) = 0, and a, b, and c are nonnegative integers, then what is a + b + c?

Guest Jan 9, 2022

#2**+1 **

Let

f(x) = ax + 3 if x > 0

f(x) = ab if x = 0

f(x) = bx + c if x < 0

f(2) = 5

we plug that into the first one beacuse x is gerater than 0...

2a+3 = 5

2a = 2

**a = 1**

f(0) = 2

we plug this one into the second one beacuse x is equal to 0...

ab = 2

1b = 2

**b = 2**

f(-2) = 0

we plug this into the third one beacuse x is less than zero...

bx + c = 0

2x + c = 0

-4 + c = 0

**c = 4 **

since the problem is asking for a + b + c.....

a+ b + c = 1 + 2 + 4 = 7

**a + b + c = 7**

Zenitsu Jan 9, 2022