Diketahui:

Fungsi $f:$ R $\rightarrow$ R dan $g:$ R $\rightarrow$ R dengan $f\left(x\right)=x-1$ dan $g\left(x-1\right)=x^2-2x+1$.

Ditanya:

Hasil dari $f\left(x-1\right)-g(x)$?

Jawab:

Diketahui $g\left(x-1\right)=x^2-2x+1$. Akan dicari $g\left(x\right)$. Dimisalkan $y=x-1$, maka $y+1=x$, sehingga

$g\left(x-1\right)=x^2-2x+1$

$\Leftrightarrow g\left(y\right)=\left(y+1\right)^2-2\left(y+1\right)+1$

$\Leftrightarrow g\left(y\right)=y^2+2y+1-2y-2+1$

$\Leftrightarrow g\left(y\right)=y^2+2y-2y+1-2+1$

$\Leftrightarrow g\left(y\right)=y^2$

Jadi $g\left(x\right)=x^2$

Karena $f\left(x\right)=x-1$, maka

$f\left(x-1\right)=\left(x-1\right)-1=x-2$

Diperoleh

$f\left(x-1\right)-g\left(x\right)=\left(x-2\right)-x^2$

$\Leftrightarrow f\left(x-1\right)-g\left(x\right)=-x^2+x-2$