Composition of Functions Worksheets - Free Printable

It looks like you've uploaded an image containing a worksheet titled "Decomposition of Functions" with several problems related to function composition and decomposition. However, since I can't view images directly, I can’t see the specific content or task in your image.

But based on the title and typical structure of such worksheets, here’s how I can help:

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🔍 What is Function Decomposition?

Function decomposition involves breaking down a complex function into simpler functions that are composed together. For example, if:
$$
h(x) = f(g(x))
$$
then $ h $ is the composition of $ f $ and $ g $. The goal in these problems is often to:
- Find $ f $ and $ g $ such that $ h(x) = f(g(x)) $
- Evaluate composite functions
- Solve for unknowns given compositions

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📝 Common Types of Problems on Such Sheets:

1. Given $ h(x) = f(g(x)) $, find possible $ f(x) $ and $ g(x) $
2. Evaluate $ (f \circ g)(x) $ or $ (g \circ f)(x) $
3. Solve equations involving function composition
4. Find inverse or simplify expressions using composition

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✔ How You Can Help Me Solve It:

Please describe the problem or type out the specific question from the image. For example:

> "Problem 1: If $ h(x) = (x^2 + 1)^3 $, find functions $ f $ and $ g $ such that $ h(x) = f(g(x)) $."

Or:

> "Given $ f(x) = x^2 $ and $ g(x) = 2x + 1 $, find $ (f \circ g)(x) $."

Once I know the exact problem, I’ll solve it step by step and explain clearly.

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💡 Tip: If you’re unsure how to decompose a function, look for an “inner” function (the one inside parentheses or being operated on), and then the “outer” function acting on it.

For example:
- $ h(x) = \sqrt{x^2 + 1} $
- Inner: $ g(x) = x^2 + 1 $
- Outer: $ f(x) = \sqrt{x} $
- So $ h(x) = f(g(x)) $

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👉 Please type the problem(s) from the image so I can assist you fully!