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Rashida was asked to determine whether 
f(x)=x^(2)-|x| is even, odd, or neither. Here is her work:
Step 1: Find expression for 
f(-x)

{:[f(-x)=(-x)^(2)-|(-x)|],[=x^(2)+|x|]:}
Step 2: Check if 
f(-x) is equal to 
f(x) or 
-f(x)

x^(2)+|x| isn't the same as 
f(x)=x^(2)-|x| or 
-f(x)=-x^(2)+|x|.
Step 3: Conclusion

f(-x) isn't equivalent to either 
f(x) or 
-f(x), so 
f is neither even nor odd.
Is Rashida's work correct? If not, what is the first step where Rashida made a mistake?
Choose 1 answer:
(A) Rashida's work is correct.
(B) Rashida's work is incorrect. She first made a mistake in Step 1.
(C) Rashida's work is incorrect. She first made a mistake in Step 2.
(D) Rashida's work is incorrect. She first made a mistake in Step 3.

Rashida was asked to determine whether f(x)=x2x f(x)=x^{2}-|x| is even, odd, or neither. Here is her work:\newlineStep 11: Find expression for f(x) f(-x) \newlinef(x)=(x)2(x)=x2+x \begin{aligned} f(-x) & =(-x)^{2}-|(-x)| \\ & =x^{2}+|x| \end{aligned} \newlineStep 22: Check if f(x) f(-x) is equal to f(x) f(x) or f(x) -f(x) \newlinex2+x x^{2}+|x| isn't the same as f(x)=x2x f(x)=x^{2}-|x| or f(x)=x2+x -f(x)=-x^{2}+|x| .\newlineStep 33: Conclusion\newlinef(x) f(-x) isn't equivalent to either f(x) f(x) or f(x) -f(x) , so f f is neither even nor odd.\newlineIs Rashida's work correct? If not, what is the first step where Rashida made a mistake?\newlineChoose 11 answer:\newline(A) Rashida's work is correct.\newline(B) Rashida's work is incorrect. She first made a mistake in Step 11.\newline(C) Rashida's work is incorrect. She first made a mistake in Step 22.\newline(D) Rashida's work is incorrect. She first made a mistake in Step 33.

Full solution

Q. Rashida was asked to determine whether f(x)=x2x f(x)=x^{2}-|x| is even, odd, or neither. Here is her work:\newlineStep 11: Find expression for f(x) f(-x) \newlinef(x)=(x)2(x)=x2+x \begin{aligned} f(-x) & =(-x)^{2}-|(-x)| \\ & =x^{2}+|x| \end{aligned} \newlineStep 22: Check if f(x) f(-x) is equal to f(x) f(x) or f(x) -f(x) \newlinex2+x x^{2}+|x| isn't the same as f(x)=x2x f(x)=x^{2}-|x| or f(x)=x2+x -f(x)=-x^{2}+|x| .\newlineStep 33: Conclusion\newlinef(x) f(-x) isn't equivalent to either f(x) f(x) or f(x) -f(x) , so f f is neither even nor odd.\newlineIs Rashida's work correct? If not, what is the first step where Rashida made a mistake?\newlineChoose 11 answer:\newline(A) Rashida's work is correct.\newline(B) Rashida's work is incorrect. She first made a mistake in Step 11.\newline(C) Rashida's work is incorrect. She first made a mistake in Step 22.\newline(D) Rashida's work is incorrect. She first made a mistake in Step 33.
  1. Find expression: Find expression for f(x)f(-x)f(x)=(x)2(x)f(-x)=(-x)^2-\lvert(-x)\rvertSince (x)2=x2(-x)^2 = x^2 and (x)=x\lvert(-x)\rvert = \lvert x \rvert, the correct expression should be:f(x)=x2xf(-x)=x^2-\lvert x \rvert

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