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# Examples of Functions

Here are a few examples of functions, and how to solve them.

Example 1: If f(x) = x2 + 2x + 1, find f(2).

Here we have to find out the value of f(x), when the value of x is given to be 2. Applying the value of x = 2 in the function, we get

f(x) = 22 + 2 x 2 + 1

=  4 + 4 + 1

= 9

Example 2: Find the value of x when the function f(x) = x2 + 4x + 3 is zero.

Given f(x) = 0, x2 + 4x + 3  = 0. We have to now solve the equation –

x2 + 4x + 3  = 0

(x + 1)(x + 3)  = 0

x = -1 or x = -3.

f(-1) = (-1)2 + 4 x -1 + 3

= 1 – 4 + 3

= 0

f(-3) = (-3)2 + 4 x -3 + 3

= 9 – 12 + 3

= 0

Note: f(x) = 0 is different from f(0). In the above example, f(x) = 0 when x = -1 or x = -3.

But f(0) = (0)2 + 4 x 0 + 3

= 3

Example 3: A function f(x) is defined as  f(x)  = Find f(1), f(2) and f(-2).

When x ≥ 1, the function is 3x + 4. So

f(1)  =  3×1 + 4  = 7

f(2)  =  3×2 + 4  = 10

But when x < 1, the function is x2. So

f(-2)  =  x2  = (-2)2  =  4

So f(1) = 7,   f(2) = 10,  and f(-2) = 4