Question

[Nguyễn Quỳnh Vân]

Cho hàm số \(y = f ( x ) = [ x ]\) với x thuộc Q .

a, Tính \(5 ( f ) 4 + 6 f (5\dfrac{1}{6})- 8f(-9,4)\) .

b, Tìm x để \(| f (x) | = 0\)

Answer 1

[Nguyễn Minh Tuấn]

*Bài làm:

a, Ta có: \(y=f\left(x\right)=|x|\)

⇒ \(\left\{{}\begin{matrix}f\left(4\right)=y=|4|=4\\f\left(5\frac{1}{6}\right)=y=|5\frac{1}{6}|=5\frac{1}{6}=\frac{31}{6}\\f\left(-9,4\right)=y=|-9,4|=9,4\end{matrix}\right.\)

⇒ \(\left\{{}\begin{matrix}5.f\left(4\right)=5y=5.4=20\\6.f\left(5\frac{1}{6}\right)=6y=6.\frac{31}{6}=31\\8.f\left(-9,4\right)=8y=8.9,4=\text{75.2‬}\end{matrix}\right.\)

⇒ \(5f\left(4\right)+6f\left(5\frac{1}{6}\right)-8f\left(-9,4\right)\) = \(20+31-75.2\) = \(\text{-24.2‬}\)

~Vậy: \(5f\left(4\right)+6f\left(5\frac{1}{6}\right)-8f\left(-9,4\right)\) = \(\text{-24.2‬}\) .

b, Ta có: \(y=f\left(x\right)=|x|\)

⇒ \(|y|=|f\left(x\right)|=||x||\)

Mà \(|f\left(x\right)|=0\) (Theo đề cho).

⇒ \(|y|=|f\left(x\right)|=||x||=0\)

⇒ \(y=f\left(x\right)=|x|=0\)

⇒ \(\left|x\right|=0\)

⇒ \(x=0\) .

~Vậy: \(x=0\) thỏa mãn đề .

➤ Chúc bạn học tốt!