Question

Classifique se as funções abaixo é função ímpar ou função par.
A) f(x)=x
B) g(x)= -x + 1
C) g(x)= x/2
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Answer 1

$\huge\boxed{\begin{array}{l}\sf f(x)\,\acute e\,par\iff f(-x)=f(x)\\\sf f(x)\,\acute e\,\acute impar\iff f(-x)=-f(x)\end{array}}$

$\large\boxed{\begin{array}{l}\rm A)~\sf f(x)=x\\\sf f(-x)=-x\\\sf mas\,x=f(x)\\\sf portanto\,f(-x)=-f(x)\implies func_{\!\!,}\tilde ao\,\acute impar\\\rm B)~\sf g(x)=-x+1\\\sf g(-x)=-(-x)+1\\\sf g(-x)=x+1\\\sf g(x)\,n\tilde ao\,\acute e\,par\,e\,nem\,\acute impar\\\sf C)~\sf g(x)=\dfrac{x}{2}\\\\\sf g(-x)=\dfrac{-x}{2}\\\\\sf g(-x)=-\dfrac{x}{2}\\\sf mas~~\dfrac{x}{2}=g(x)\\\\\sf ent\tilde ao\\\sf g(-x)=-g(x)\implies func_{\!\!,}\tilde ao\,\acute impar.\end{array}}$