Understanding f(g(x)) | Breaking Down Composition of Functions in Math

f(g(x))

To understand the expression f(g(x)), we need to break it down step by step

To understand the expression f(g(x)), we need to break it down step by step.

Let’s start with g(x).

The notation g(x) indicates that x is being input into the function g. So, g(x) means that we are taking the input x and passing it through the function g.

Now, let’s consider f.

Similarly, f(g(x)) means that the output of g(x) is being taken as the input of the function f. In other words, the output of g(x) is substituted into the function f.

To illustrate this with an example, let’s assume that:

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

First, we’ll find g(x) by substituting x into the function:

g(x) = 2x + 3

Now, we’ll take the output of g(x) and substitute it into the function f:

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

We already know that g(x) is equal to 2x + 3. So, we substitute this expression into f:

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

Now, we can expand and simplify this expression:

f(2x + 3) = (2x + 3)(2x + 3) = 4x^2 + 12x + 9

So, f(g(x)) simplifies to 4x^2 + 12x + 9.

In summary, the expression f(g(x)) indicates that the output of g(x) is being substituted into the function f. The resulting expression represents the composition of the two functions.

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