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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?

 Jan 9, 2022
 #1
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a + b + c = 18.

 Jan 9, 2022
 #2
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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

 Jan 9, 2022

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