solve for x

Question

Let h(x) = |x| − 2x + 5. Find all solutions to the equation h(x − 1) = x − 3.
this is what i have but it is not correct...

x-3=x-1-2x-2+5
x=-x+5
2x=5
x=2.5 and x is greater than or equal to 0
then
x-3=-x+1+2x+2+5
x-3=x+8
which would not be answer bc nothing cannot equal 8... where am I going wrong?

Answer 1

It's hard to help with this without giving away the game.

 

Consider the graph of the absolute value of x. It has a vee shape. When x is positive it's a line with slope of +1 and y-intercept of 0. When x is negative it's a line with a slope of -1 and y-intercept of 0. Get some graph paper and plot this. Now think about what happens when we add a constant to a function -- the line moves, right? Ah, but what direction does it move? up? down? left? right?

 

Let's pick an actual value for the constant and plot the new function, say 5.

 

so, y = ⌈x⌉ + 5  (the absolute value of x plus 5).  Now put -2x in the function. The line(s) will move again.

 

If you're still stuck, try plotting some points and connect them.

 

Now what does the equation h(x-1) = x - 3 mean? Try looking up "composition of functions" in your text book and study an example.

 

Post a response to this message if you have more questions.