Definisi operasi fungsi
Misal f:ℝ\toℝ dan g:ℝ\toℝ dua fungsi dan a\inℝ. Maka:
a. (f\pm g)(x) = f(x) \pm g(x)
b. (af)(x) = a f(x)
c. (fg)(x) = f(x)g(x)
d. (\frac{f}{g})(x)= \frac{f(x)}{g(x)}, g(x) \neq 0
Catatan:
a. Jika D(f+g) = D(f) \cap D(g)
b. Jika D(af) = D(f)
c. Jika D(fg) = D(f) \cap D(g) dan,
d. Jika D(\frac{f}{g})(x)=D(f) \cap D(g), g(x) \neq 0
Contoh:
Diketahui:
f(x)=x^2, D(f) = ℝ dan g(x) = 3, D(g) = ℝ. Maka:
\begin{align}
a). (f+g)(x) &= f(x) + g(x)\\
&=x^2 + 3\\
D(f+g)&= ℝ\capℝ = ℝ
\end{align}
\begin{align}
b). (f-g)(x) &= f(x) - g(x)\\
&=x^2 - 3\\
D(f+g)&= ℝ\capℝ = ℝ
\end{align}
\begin{align}
c). (5f)(x) &= 5f(x)\\
&=5x^2\\
D(5f)&= ℝ
\end{align}
\begin{align}
d). (fg)(x) &= f(x) g(x)\\
&=(x^2) (3)\\
&= 3x^2\\
D(fg)&= ℝ\capℝ = ℝ
\end{align}
\begin{align}
e). (\frac{f}{g})(x) &= \frac{f(x)} {g(x)}\\
&=\frac {x^2} {3}\\
D(\frac{f}{g})&= ℝ\capℝ = ℝ
\end{align}
Silahkan jika ada yang ingin bertanya dan berdiskusi. Terima kasih.