Function

Function is a relationship where a set of inputs (domain) determine a set of possible outputs (range).  The function of  \(\large{ f \left( x \right) = 5\;x }\)  is  \(\large{ f \left( x \right) }\) , the function name is  \(\large{ f }\) , the input value is  \(\large{ \left( x \right) }\) , and the output is  \(\large{ 5\;x }\) .

 

• \(\large{\; f \left( x \right) = 5\;x }\) , find  \(\large{ f \left( 2 \right) }\)
• \(\large{\; f \left( 2 \right) = 5\left( 2 \right) = 10 }\)

 

• \(\large{\; f \left( x \right) = 5x + 3x^2 - 4 + 3 }\) , find  \(\large{ f \left( 2y + 5 \right) }\)
• \(\large{\; f \left( 2y + 5 \right) = 5\left( 2y + 5 \right) + 3\left( 2y + 5 \right)^2 - 4 + 3 }\)
• \(\large{\;                                = 10y + 25  + 3\left( 4y^2 + 12y  + 25 \right) - 4 + 3 }\)
• \(\large{\;                                = 10y + 25  + 12y^2 + 36y + 75 - 4 + 3 }\)
• \(\large{\;                                = 46y + 99  + 12y^2  }\)