How Do Absolute Values Affect Solving Function Equations?

[PhysicslyDSBL]

Homework Statement

I do not see how the two equations in each example are related, what should I do with them? (the l's are absolute value brackets):

a) Let g(x) = 3x - 3 + l x+5 l. Find all values of a which satisfy the equation:

g(a) = 2a +8


b) Let h(x) = l x l - 3x + 4. Find all solutions to the equation :

h(x - 1) = x - 2


I know how to find an equation of the following:

x + l 2x-1 l, find f(x) = 8

x + l 2x-1 l = 8

l 2x-1 l = 8-x

2x-1 = 8-x or -2x+1= 8-x
x=3 x=-7

 

[Mark44]

For part a, you have the formula for g(x), so g(a) = 3a -3 + |a + 3|

Set that expression equal to 2a + 8. Isolate the absolute value expression on one side, and keep in mind that |x| = x if x >= 0 and |x| = -x if x < 0.