Bài 1:

\(f\left(x\right)=5x-3.\)

+ \(f\left(x\right)=0\)

\(\Rightarrow5x-3=0\)

\(\Rightarrow5x=0+3\)

\(\Rightarrow5x=3\)

\(\Rightarrow x=3:5\)

\(\Rightarrow x=\frac{3}{5}\)

Vậy \(x=\frac{3}{5}.\)

+ \(f\left(x\right)=1\)

\(\Rightarrow5x-3=1\)

\(\Rightarrow5x=1+3\)

\(\Rightarrow5x=4\)

\(\Rightarrow x=4:5\)

\(\Rightarrow x=\frac{4}{5}\)

Vậy \(x=\frac{4}{5}.\)

+ \(f\left(x\right)=-2010\)

\(\Rightarrow5x-3=-2010\)

\(\Rightarrow5x=\left(-2010\right)+3\)

\(\Rightarrow5x=-2007\)

\(\Rightarrow x=\left(-2007\right):5\)

\(\Rightarrow x=-\frac{2007}{5}\)

Vậy \(x=-\frac{2007}{5}.\)

Làm tương tự với \(f\left(x\right)=2011.\)

Chúc bạn học tốt!

a: \(f\left(1\right)=\dfrac{1-1}{1-2}=-1\)

\(f\left(-1\right)=\dfrac{-1-1}{-1-2}=-\dfrac{2}{-3}=\dfrac{2}{3}\)

\(f\left(0\right)=\dfrac{0-1}{0-2}=\dfrac{1}{2}\)

\(f\left(2\right)=\dfrac{2-1}{2-2}=\varnothing\)

b: f(x)=2 nên x-1=2x-4

=>2x-4=x-1

=>x=3

c: Để y là số ngyên thì \(x-2+1⋮x-2\)

\(\Leftrightarrow x-2\in\left\{1;-1\right\}\)

hay \(x\in\left\{3;1\right\}\)

Giỏi quá ha!!!

\(y=f\left(x\right)=\dfrac{x-1}{x-2}\)

a)

\(y=f\left(1\right)=\dfrac{1-1}{1-2}=\dfrac{0}{-1}=0\)

\(y=f\left(-1\right)=\dfrac{\left(-1\right)-1}{\left(-1\right)-2}=\dfrac{-1-1}{-1-2}=\dfrac{-\left(1+1\right)}{-\left(1+2\right)}=\dfrac{-2}{-3}=\dfrac{2}{3}\)

\(y=f\left(0\right)=\dfrac{0-1}{0-2}=\dfrac{-1}{-2}=\dfrac{1}{2}\)

@CTV

a) \(f\left(0\right)\Rightarrow y=\left|0^2-1\right|=\left|-1\right|=1\)

\(f\left(-1\right)\Rightarrow y=\left|\left(-1\right)^2-1\right|=\left|1-1\right|=\left|0\right|=0\)

\(f\left(1\right)\Rightarrow y=\left|1^2-1\right|=\left|1-1\right|=\left|0\right|=0\)

\(f\left(\dfrac{1}{2}\right)\Rightarrow y=\left|\left(\dfrac{1}{2}\right)^2-1\right|=\left|\dfrac{1}{4}-1\right|=\left|\dfrac{-3}{4}\right|=\dfrac{3}{4}\)

b) ta có : \(y=7\Rightarrow\left|x^2-1\right|=7\Leftrightarrow\) \(\left\{{}\begin{matrix}x^2-1=7\\x^2-1=-7\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x^2=8\\x^2=-6\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\left\{{}\begin{matrix}x=\sqrt{8}\\x=-\sqrt{8}\end{matrix}\right.\\x\in\varnothing\end{matrix}\right.\) vậy \(x=\sqrt{8};x=-\sqrt{8}\)

ta có : \(y=17\Leftrightarrow\left|x^2-1\right|=17\Leftrightarrow\) \(\left\{{}\begin{matrix}x^2-1=17\\x^2-1=-17\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x^2=18\\x^2=-16\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\left\{{}\begin{matrix}x=\sqrt{18}\\x=-\sqrt{18}\end{matrix}\right.\\x\in\varnothing\end{matrix}\right.\) vậy \(x=\sqrt{18};x=-\sqrt{18}\)

F(2)+F(1)=8

=>\(2^2\left(m^2+1\right)+2\left(m^2+1\right)-5+m^2+1+2\left(m^2+1\right)-5=8\)

=>\(8\left(m^2+1\right)+m^2+1-10=8\)

=>\(9\left(m^2+1\right)=18\)

=>\(m^2+1=2\)

=>\(m^2=1\)

=>\(\left[{}\begin{matrix}m=1\\m=-1\end{matrix}\right.\)

\(y=f\left(x\right)=\dfrac{5}{x-1}\)

a) ĐKXĐ khi: \(x-1\ne0\) \(\Leftrightarrow x\ne1\)

b)

\(y=f\left(-2\right)=\dfrac{5}{-2-1}=\dfrac{5}{-\left(2+1\right)}=\dfrac{5}{-3}=\dfrac{-5}{3}\)

\(y=f\left(\dfrac{1}{3}\right)=\dfrac{5}{\dfrac{1}{3}-1}=\dfrac{5}{\dfrac{1}{3}-\dfrac{3}{3}}=\dfrac{5}{\dfrac{-2}{3}}=\dfrac{-15}{2}\)

c)

* \(y=f\left(x\right)=\dfrac{5}{x-1}=-1\)

\(\Rightarrow x-1=5:\left(-1\right)\)

\(\Rightarrow x-1=-5\)

\(\Rightarrow x=-5+1\)

\(\Rightarrow x=-\left(5-1\right)\)

\(\Rightarrow x=-4\)

Vậy \(y=-1\) thì \(x=-4\)

* \(y=f\left(x\right)=\dfrac{5}{x-1}=1\)

\(\Rightarrow x-1=5:1\)

\(\Rightarrow x-1=5\)

\(\Rightarrow x=5+1\)

\(\Rightarrow x=6\)

Vậy \(y=1\) thì \(x=6\)

* \(y=f\left(x\right)=\dfrac{5}{x-1}=\dfrac{1}{5}\)

\(\Rightarrow x-1=5:\dfrac{1}{5}\)

\(\Rightarrow x-1=5.5\)

\(\Rightarrow x-1=25\)

\(\Rightarrow x=25+1\)

\(\Rightarrow x=26\)

Vậy \(y=\dfrac{1}{5}\) thì \(x=26\)

a) f(0)= -5: f(-1)= -3: f(căn 2)= -1: f(-1/2)= -6

b) y= -5 thì x=0: y= 3 thì x= 2: y= -1 thì x=1.414213562: y= -6 thì x= Không tính được

a/ y=f(x)=-2x+3

f(-2)=-2*(-2)+3=7

f(-1)=-2*(-1)+3=5

f(0)=-2*0+3=3

f(-1/2)=-2*-1/2+3=4

f(1/2)=-2*1/2+3=2

b/y=g(x)=x^2-1

g(-1)=-1^2-1=-2

g(0)=0^2-1=-1

g(2)=2^2-1=3

a) f(-2)=+2.(-2)+3=7

f(-1)=2.(-1)+3=5

f(0)=2.0+3=3

f(-1/2)=2.(-1/2)+3=4

f(1/2)=2.1/2+3=2

b) g(-1)=-1^2-1=-2

g(0)=0^2-1=1

g(1)=1^2-1=0

g(2)=2^2-1=3

CHÚC BẠN HC TỐT!!