Solving Function Notation

Function help to show relationship between variable (quantities). The variable in the function may be either dependent or independent. Each function consists of input and output data. For solving the function notation is to change the input data in function. For Example: Let take the function as y = x + 13, Here the input of the function is x and output of the function is y. Thus x indicated as independent variable and y indicated as dependent variable. The given equation involving x and y that can be written in form y = f(x) and referred that y is the function. y = f(x) = x + 13. In this article, we will discuss about how for solving function notation with some example problem.

Example Problem – Solving Function Notation:

Example 1:

Solving the function notation of the function f (x) = 3x2 + 3x + 12 when x = 2

Solution:

Given: f (x) = 3x2 + 3x + 12

To find: f(2), here x = 2

Step 1:

Substitute the value of 2 in place of variable x.

f (2) = 3 * (2)2 + 3(2) + 12

f (2) = (3 * 4) + 6 + 12

f (2) = 12 + 6 + 12

f (2) = 30

Answer: f (2) = 30

Example 2:

Solving the function notation f(x) = x2 + 3 when x = g(x). The function g(x) = x – 1.

Solution:

Given: f(x) = x2 + 3

To find: f(g(x))

Here input of the function f(x) is g(x)

Therefore x = g(x)

Step 1:

Substitute the g(x) in place of x.

g(x) = x – 1

Step 2:

f(x) = x2 + 3

f(g(x)) = x2 + 3

= (x - 1)2 + 3

= (x2) – 2x + 1 + 3

= x2 – 2x + 4

Thus the value of f(g(x)) = x2 – 2x + 4.

Answer: f(x) = x2 – 2x + 4

Practice Problem – Solving Function Notation:

Problem 1:

If y = f(x) = 3x + 4, then what is the value of y when x = 4

Answer: y = 16

Problem 2:

Solving f(x) = x2 + 3x + 4 when 3f(-2)

Answer: 6