Function Notation Formula

Functions or Functional Notations are referred by the letter ‘f’ and written as f(x), sometimes in the form of g(x), h(a) etc.

Question 1: Represent y =

\begin{array}{l} x^{2} \end{array}

+ 4x + 1 using function notation and find the value of y at x = 3.

Solution:

Given function is,
y =

\begin{array}{l} x^{2} \end{array}

+ 4x + 1
By using function notation,
f(x) =

\begin{array}{l} x^{2} \end{array}

+ 4x + 1
Value of y at x = 3 means f(3).
So, f(3) =

\begin{array}{l} 3^{2} \end{array}

+ 4

\begin{array}{l} \times \end{array}

3 + 1 = 9 + 12 + 1 = 22

Question 2: Represent the given function y =

\begin{array}{l} x^{3} \end{array}

– 4x using function notation and find the value of y at x = 2.

Solution:

Given function is,
y =

\begin{array}{l} x^{3} \end{array}

– 4x
By using function notation,
f(x) =

\begin{array}{l} x^{3} \end{array}

– 4x
The value of y at x = 2 means f(2).
Therefore, f(2) =

\begin{array}{l} 2^{3} \end{array}

– 4

\begin{array}{l} \times \end{array}

2 = 8 -8 = 0