Understanding f(x+3) in Mathematics | Expression, Function, and Horizontal Shift

f(x+3)

In mathematics, f(x+3) represents an expression or function where x is replaced by (x+3)

In mathematics, f(x+3) represents an expression or function where x is replaced by (x+3). This means that whatever the original function f(x) was, we are now evaluating it or obtaining the value of the function when the input is increased by 3.

To understand this better, let’s take an example. Suppose we have the function f(x) = 2x. If we want to find f(x+3), we substitute (x+3) in place of x, like so:

f(x+3) = 2(x+3)

Now we simplify the expression by distributing the 2:

f(x+3) = 2x + 6

So, f(x+3) of the original function f(x) = 2x is equal to 2x + 6 when x is increased by 3.

It is important to note that f(x+3) represents a horizontal shift of the original function f(x) by 3 units to the left. The “(x+3)” part inside the function notation modifies the input value of x.

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