{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Sección 4.3\n",
        "Emplearémos sympy para mostrar las composiciones de dos funciones F y G dadas."
      ],
      "metadata": {
        "id": "qGHeQyka-zvr"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 76
        },
        "id": "opW6A2_g4Lzx",
        "outputId": "7a519c00-ca54-468f-eb92-b8cdd9f9ee46"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "f(g(x)):\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "sqrt(1 - 1/x**2)"
            ],
            "text/latex": "$\\displaystyle \\sqrt{1 - \\frac{1}{x^{2}}}$"
          },
          "metadata": {}
        }
      ],
      "source": [
        "#import sympy as sym\n",
        "from sympy import symbols, sqrt\n",
        "\n",
        "x = symbols('x')\n",
        "\n",
        "# 1. Definimos las expresiones de las funciones\n",
        "f = sqrt(1 - x**2)\n",
        "g = 1 / x\n",
        "\n",
        "# 2. Calculamos las composiciones usando .subs()\n",
        "# fog significa f(g(x)): En 'f', sustituimos la 'x' por 'g'\n",
        "fog = f.subs(x, g)\n",
        "\n",
        "# gof significa g(f(x)): En 'g', sustituimos la 'x' por 'f'\n",
        "gof = g.subs(x, f)\n",
        "\n",
        "# 3. Mostramos los fog:\n",
        "print(f\"f(g(x)):\")\n",
        "display(fog)\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Ahora mostramos gof\n",
        "print(f\"g(f(x)):\")\n",
        "display(gof)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 72
        },
        "id": "iu9i4iDY5LpA",
        "outputId": "dc9e3ffc-c37f-4823-c7de-9c576777e823"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "g(f(x)):\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "1/sqrt(1 - x**2)"
            ],
            "text/latex": "$\\displaystyle \\frac{1}{\\sqrt{1 - x^{2}}}$"
          },
          "metadata": {}
        }
      ]
    }
  ]
}