Expert: Paul Klarreich - 12/27/2011

Question
the function f(x)=/ax-1/ - /bx+2/ is such that f(-1/2)=1 and f(1/3) = -7/3. given that 0 is less than a less than or equal to 3 and 0 less than b less 4, find the values of a and b.

Answer
Questioner: kwibisa
Country: Luapula, Zambia
Category: Advanced Math
Private: No
Subject: maths
Question: the function f(x)=/ax-1/ - /bx+2/ is such that f(-1/2)=1 and f(1/3) = -7/3. given that 0 < a <= 3 and 0 < b < 4, find the values of a and b.
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Try substituting:

f(x) = |ax - 1| - |bx + 2|


f(-1/2) = |a(-1/2) - 1| - |b(-1/2) + 2|

f(-1/2) = |- a/2 - 1| - |- b/2 + 2|

Now do some thinking:

If a > 0, -a/2 < 0

BTW, remember that we math-types write " > 0 " to mean "is positive", and stuff like that.

So |- a/2 - 1| is | neg |, and is a/2 + 1

If  b < 4, b/2 < 2, -b/2 > -2,  -b/2 + 2 > 0, so

| - b/2 + 2 | is | positive | and is (-b/2 + 2).

Now write:

f(-1/2) = a/2 + 1 - (-b/2 + 2) = 1   << it said f(-1/2) = 1, didn't it?

a/2 + 1 + b/2 - 2 = 1

a/2 - 1 + b/2 = 1

a/2 + b/2 = 2

a + b = 4

That is one equation in a,b.
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Now do the same thinking for  f(1/3) and produce a second equation.  You're on your way.

Let me know if you get stuck.