Test 2 Section 5 - #14 (page 468)

Tough one (grid-ins usually are). The solution to this one, though, can be found by PLUGGING IN (with a little BACKSOLVE flavor added in for good measure)! Just start by trying any number for x. How about x = 3? Just to be clear, we're looking for f(3) to be LESS THAN 3 (that's what they say in the question: f(a) < a).

f(x) = |3x - 17|

f(3) = |3(3) - 17|

f(3) = |9-17|

f(3) = |-8|

f(3) = 8

Ok, so that didn't work; 8 is not less than 3. But here's where that BACKSOLVE flavor comes in: now we have a better idea of how the pieces fit together. We want x to get a little bigger, so that 3x gets closer to 17.  That way, f(x) will be small.  Why not try x = 5 next?

f(5) = |3(5) - 17|

f(5) = |15-17|

f(5) = |-2|

f(5) = 2

GREAT! 2 < 5, so x = 5 works! (A few other numbers will work too: anything between 4.25 and 8.5...though you'd probably be best to stick with integers and just try 5, 6, or 7.)