Expert: Abe Mantell - 12/31/2007

Question
Let f(x)= êx-a ê+ a and g(x)= 5x +a where a is a  positive constant,
(a)   Use algebra to find, in terms of a, the coordinates of the points where the graphs of f and g intersect.
(b)   Find an expression for f(g(x)).
(c)   Solve, for x in terms of a, the equation
          f(g(x))=7a.


Answer
Hello again Nivedha,

OK, so you meant:
f(x)=|x-a|+a, yes??  If so, then...
a) f(x)=g(x) ==> |x-a|+a=5x+a ==> |x-a|=5x
-- ==> x-a=5x, if x>=a OR -(x-a)=5x, if x<a
-- either: x=-a/4, if x>=a OR x=a/6, if x<a
-- however, since a>0, that means -a/4 is negative,
-- and then x would not be greater than or equal to a,
-- so the only solution is x=a/6 in this case.

OK?

Happy New Year!  :-)

Abe