Question

Considere uma função modular f(x) = |2x + 5| . Seja a≠b e f(a)=f(b)= 3, podemos afirmar que (a.b)² vale: A) 9 B) 25 C) 16 D) 36

Answer 1

$\boxed{\begin{array}{l}\sf f(x)=|2x+5|\\\sf f(a)=|2a+5|\\\sf |2a+5|=3\\\sf 2a+5=3\\\sf 2a=3-5\\\sf 2a=-2\\\sf a=-\dfrac{2}{2}=-1\\\sf 2a+5=-3\\\sf 2a=-5-3\\\sf 2a=-8\\\sf a=-\dfrac{8}{2}=-4\end{array}}$

$\boxed{\begin{array}{l}\sf f(b)=|2b+5|\\\sf |2b+5|=3\\\sf 2b+5=3\\\sf 2b=3-5\\\sf 2b=-2\\\sf b=-\dfrac{2}{2}\\\sf b=-1\\\sf 2b+5=-3\\\sf 2b=-3-5\\\sf 2b=-8\\\sf b=-\dfrac{8}{2}\\\sf b=-4\end{array}}$

$\Large\boxed{\begin{array}{l}\sf fazendo~a=-4~e~b=-1~temos:\\\sf (a\cdot b)^2=(-4\cdot-1)^2=4^2=16\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~C}}}}\end{array}}$