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Which of the following is true about F(x)?

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by himu » Tue Jul 09, 2013 8:07 pm
Function F(x) is defined as follows:

if x is positive or 0 then F(x)=1−x;

if x is negative then F(x)=x−1.

Which of the following is true about F(x)?

I. F(|x|)=|F(x)|
II. F(x)=F(−x)
III. |F(x+1)|=|x|
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by [email protected] » Wed Jul 10, 2013 7:34 am
Hi himu,

Roman Numeral questions can often be solved by proving the opposite of what the question asks for and then eliminating answers. The 5 answers to this question would be useful to know in that you could gauge the frequency of each roman numeral and likely avoid some of the work.

Since this question asks what is true, you goal is to prove what is NOT necessarily true:

I. If x = -2 then
F (2) = -1
|F(-2)| = 3
Roman numeral I is NOT TRUE

II. If x =1/2 then
F(1/2) = 1/2
F(-1/2) = -3/2
Roman numeral II is NOT TRUE

III. This Roman numeral appears to be TRUE. Try testing it out and see.

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by snigdha1605 » Wed Jul 10, 2013 9:30 am
Function F(x) is defined as follows:

if x is positive or 0 then F(x)=1-x;

if x is negative then F(x)=x-1.

Which of the following is true about F(x)?

I. F(|x|)=|F(x)|
II. F(x)=F(-x)
III. |F(x+1)|=|x|
For III -
If we solve with x= 0 , the equation holds

Left side of eq - |F(0+1)| = |F(1)| = |1-1| = 0
Right side of eq - |0| = 0
[/quote]
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