wholelottalove wrote:If f(x) = x-5 and g(x) = 5-x, what is the value of |f(x)| - |g(x)| + |f(g(x)|?
A. |x - 10|
B. 3x + 10
C. |x|
D. |x - 5|
E. x
To make the problem and solution easier to follow, I've rephrased the question stem and replaced a and b with x.
When the answer choices involve absolute value, I recommend plugging in a NEGATIVE number.
Let x=-1.
f(x):
Since f(x) = x-5, we get:
f(-1) = -1 - 5 = -6.
g(x):
Since g(x) = 5-x, we get:
g(-1) = 5 - (-1) = 6.
f(g(x)):
Work from the INSIDE OUT.
Since g(x) = 6, we get:
f(g(x)) = f(6).
Since f(x) = x-5, we get:
f(6) = 6-5 = 1.
Thus:
f(g(x)) = 1.
Plugging these values into the given expression, we get:
|f(x)| - |g(x)| + |f(g(x)| = |-6| - |6| + |1| = 1. This is our target.
Now we plug x=-1 into the answers to which yields our target of 1.
Only
C works:
|x| = |-1| = 1.
The correct answer is
C.
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