Operations of Functions

Notes

Operations of Functions
\((f+g)(x) = f(x) +g(x)\)
\((f-g)(x) = f(x) -g(x)\)
\((f \cdot g)(x) = f(x) ・ g(x)\)
\(\left(\frac{f}{g} \right)(x) = \displaystyle\frac{f(x)}{g(x)}\)
\((f \circ g)(x) = f(g(x))\)

 

Practice Problems

Let \(f(x)=5x+3,\,\, g(x)=3x+5,\,\, h(x)=x^2+10\)

\(\textbf{1)}\) \((f+g)(3)\)Link to Youtube Video Solving Question Number 1
\(\textbf{2)}\) \((f-g)(4)\)
\(\textbf{3)}\) \((f \cdot g)(-1)\)
\(\textbf{4)}\) \(\left(\frac{h}{f} \right)(3)\)
\(\textbf{5)}\) \((f+h)(-1)\)

 

Let \(f(x)=5x+3,\,\, g(x)=3x+5,\,\, h(x)=x^2+10\)

\(\textbf{6)}\) \((f-g)(x)\)Link to Youtube Video Solving Question Number 6
\(\textbf{7)}\) \((f \cdot g)(x)\)
\(\textbf{8)}\) \(\left(\frac{f}{g} \right)(x)\)
\(\textbf{9)}\) \((g+h)(2x)\)
\(\textbf{10)}\) \((f-g)(2x)\)

 

Let \(f(x)=5x+3,\,\, g(x)=3x+5,\,\, h(x)=x^2+10\)

\(\textbf{11)}\) \((f+g)(x)\)
\(\textbf{12)}\) \((f \cdot f)(x)\)
\(\textbf{13)}\) \(\left(\frac{g}{f} \right)(x)\)
\(\textbf{14)}\) \((g \circ h)(x)\)
\(\textbf{15)}\) \((h \circ g)(x)\)

 

See Related Pages\(\)

\(\bullet\text{ Composite Functions}\)
\(\,\,\,\,\,\,\,\,(f\circ g)(x)=f(g(x))\)
\(\bullet\text{ Inverse Functions and Relations}\)
\(\,\,\,\,\,\,\,\,f^{-1}(x)=\frac{x+3}{2}\)

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