関数合成計算機
与えられたx値で2つの関数についてf(x)、g(x)、f(g(x))、g(f(x))を評価し、各合成の段階的な導出を表示します。
入力
xの関数。標準的な数学記法で記述（^は累乗、sqrt()、sin()など）。
xの第2の関数。同じ記法で記述。
両方の関数とその合成を評価するx値。
出力
このツールを使う他の方法
REST API
curl -X POST https://api.iotools.cloud/v1/tool/function-composition-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"functionF": "x + 3",
"functionG": "x - 3",
"x": "5"
}'ご自身のアカウントのキーに差し替えてください。ツールのフィールドがそのままリクエストボディになります——ラッパーはありません。
AIエージェントに依頼する
Use the IOTools `function-composition-calculator` tool (Function Composition Calculator) on this input:
YOUR_INPUT_HEREIOTools MCPサーバーに接続された任意のエージェントにこれを貼り付け、入力内容を追加してください。
埋め込みウィジェット
<iframe
src="https://iotools.cloud/embed/function-composition-calculator/"
width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
title="関数合成計算機 — iotools.cloud"
sandbox="allow-scripts allow-forms allow-same-origin allow-downloads allow-popups allow-popups-to-escape-sandbox"
allow="clipboard-write"
style="width:100%;border:1px solid #e5e7eb;border-radius:12px;overflow:hidden"></iframe>
<script src="https://iotools.cloud/embed.js" async></script>ご自身のページに貼り付けるだけ——無料、キー不要、リンクを掲載するだけです。
| API/MCP 1回あたりの費用 | 5クレジットから |
|---|---|
| クレジットが足りませんか? | 料金を見る |
次の方法でも利用可能
ガイド
The Function Composition Calculator evaluates two functions, f(x) and g(x), at a given value of x, then combines them into the composite functions f(g(x)) and g(f(x)) — showing every substitution along the way.
It's built for algebra and precalculus students checking composition homework, and anyone who needs to verify how two functions combine without working through the algebra by hand.
How to use it
- Enter f(x) and g(x) in terms of x — standard math notation works:
^for powers, plussqrt(),sin(),cos(),log(), and the other functions supported by mathjs's expression parser. - Enter the x value to evaluate both functions and their compositions at.
- Read f(x), g(x), f(g(x)), and g(f(x)) for the four evaluated results.
- Step-by-Step Derivation shows the substitution behind each composition.
Results update automatically as you type. For example, f(x) = x + 3, g(x) = x - 3, at x = 5 gives f(x) = 8, g(x) = 2, f(g(x)) = 5, and g(f(x)) = 5 — since these two functions are inverses of each other, both compositions return the original x.
What is function composition?
Composing two functions means feeding the output of one into the other. f(g(x)) means "first apply g to x, then apply f to that result" — computed as f(g(x)), not f(x) · g(x). g(f(x)) reverses the order: apply f first, then g. The two compositions are generally not equal — composition isn't commutative, which is exactly why this calculator computes both.
Why do f(g(x)) and g(f(x)) usually differ?
Because the order of substitution changes which expression gets plugged into which. For f(x) = 2x + 1 and g(x) = x^2, f(g(x)) = 2x^2 + 1 while g(f(x)) = (2x + 1)^2 — entirely different expressions that only coincide at specific x values, if at all. Checking both, as this calculator does, is the fastest way to confirm which composition a problem is actually asking for.
What functions can I enter?
Anything mathjs's expression evaluator understands: polynomials (x^3 - 2x + 1), trigonometric functions (sin(x), cos(x), tan(x)), roots and logarithms (sqrt(x), log(x)), and combinations of these. Angles in trig functions are in radians by default — write pi for π. If a composition isn't defined at your chosen x (for example, f(x) = sqrt(x) composed with a g(x) that goes negative), the calculator flags it rather than showing an invalid result.
To check whether a function is symmetric rather than compose two of them, see the Function Odd/Even/Neither Checker. To evaluate arbitrary math expressions directly, see the Math Evaluator.
Privacy
This calculator runs entirely in your browser. Your functions and x value are never uploaded, logged, or stored — the computation happens locally on your device.