If f(x) = 3x - 5 and g(x) = 2x + 1, then the composite function (f o g)(x) is equal to:


To find the composite function \((f \circ g)(x)\), you need to substitute \(g(x)\) into \(f(x)\). In other words, you evaluate \(f\) at \(g(x)\).

Given:
- \(f(x) = 3x - 5\)
- \(g(x) = 2x + 1\)

We want to find \(f(g(x))\). This means substituting \(g(x) = 2x + 1\) into \(f(x)\):

\[
f(g(x)) = f(2x + 1)
\]

Now, replace \(x\) in \(f(x) = 3x - 5\) with \(2x + 1\):

\[
f(2x + 1) = 3(2x + 1) - 5
\]

Distribute the 3:

\[
f(2x + 1) = 6x + 3 - 5
\]

Simplify:

\[
f(2x + 1) = 6x - 2
\]

So, the composite function \((f \circ g)(x)\) is:

\[
(f \circ g)(x) = 6x - 2
\]

Would you like more details on composite functions or have any other questions?

Here are 5 related questions to explore further:
1. What is the composite function \((g \circ f)(x)\)?
2. How do you find the inverse of a composite function?
3. What happens if you compose more than two functions, like \((h \circ f \circ g)(x)\)?
4. Can you graph composite functions and what do they look like?
5. How do you solve composite functions if the output is known (e.g., \((f \circ g)(x) = 10\))?

**Tip**: When working with composite functions, always follow the order of operations, starting from the inside function first.

If f(x) = 3x - 5 and g(x) = 2x + 1, then the composite function (f o g)(x) is equal to:

Discover how to find the composite function (f o g)(x) when f(x) = 3x - 5 and g(x) = 2x + 1. This example demonstrates the steps to substitute and simplify functions, applying key algebraic concepts. Ideal for students in Grades 9-11.

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