Soit \(f\) la fonction définie sur \(\mathbb{R}\) par : \(f: x \mapsto x^{5} + \operatorname{sin}{\left (x \right )}\). Le graphe de \(f\) est donné ci-dessous :
{"init": {"range": [[-10, 10], [-5, 5]], "hasGraph": true, "xLabel": "", "yLabel": "", "num_points": null, "labelStep": [1, 5], "tickStep": [1, 1], "gridOpacity": 0.1, "gridStep": [1, 1], "axisOpacity": 0.5, "unityLabels": true, "axisArrows": "->", "settings": {"scale": [25, 25], "range_draw": [[-10, 10], [-5, 5]]}, "scale": [25, 25], "range_draw": [[-10, 10], [-5, 5]], "x_max": 10, "x_min": -10}, "plot": [["function(x){ return Math.pow(x, 5) + Math.sin(x);}", [-10, 10], {}]]}
Soit \(g\) la fonction définie sur \(\mathbb{R}\) par : \(g: x \mapsto \left(\operatorname{cos}{\left (x \right )}\right)^{2}\). Le graphe de \(g\) est donné ci-dessous :
{"init": {"range": [[-10, 10], [-5, 5]], "hasGraph": true, "xLabel": "", "yLabel": "", "num_points": null, "labelStep": [1, 5], "tickStep": [1, 1], "gridOpacity": 0.1, "gridStep": [1, 1], "axisOpacity": 0.5, "unityLabels": true, "axisArrows": "->", "settings": {"scale": [25, 25], "range_draw": [[-10, 10], [-5, 5]]}, "scale": [25, 25], "range_draw": [[-10, 10], [-5, 5]], "x_max": 10, "x_min": -10}, "plot": [["function(x){ return Math.pow(Math.cos(x), 2);}", [-10, 10], {}]]}
Soit \(h\) la fonction définie sur \(\mathbb{R}\) par : \(h: x \mapsto -1 + \dfrac{1}{x}\). Le graphe de \(h\) est donné ci-dessous :
{"init": {"range": [[-10, 10], [-5, 5]], "hasGraph": true, "xLabel": "", "yLabel": "", "num_points": null, "labelStep": [1, 5], "tickStep": [1, 1], "gridOpacity": 0.1, "gridStep": [1, 1], "axisOpacity": 0.5, "unityLabels": true, "axisArrows": "->", "settings": {"scale": [25, 25], "range_draw": [[-10, 10], [-5, 5]]}, "scale": [25, 25], "range_draw": [[-10, 10], [-5, 5]], "x_max": 10, "x_min": -10}, "plot": [["function(x){ return -1 + 1/x;}", [-10, 10], {}]]}
Soit \(j\) la fonction définie sur \(\mathbb{R}\) par : \(j: x \mapsto 2\). Le graphe de \(j\) est donné ci-dessous :
{"init": {"range": [[-10, 10], [-5, 5]], "hasGraph": true, "xLabel": "", "yLabel": "", "num_points": null, "labelStep": [1, 5], "tickStep": [1, 1], "gridOpacity": 0.1, "gridStep": [1, 1], "axisOpacity": 0.5, "unityLabels": true, "axisArrows": "->", "settings": {"scale": [25, 25], "range_draw": [[-10, 10], [-5, 5]]}, "scale": [25, 25], "range_draw": [[-10, 10], [-5, 5]], "x_max": 10, "x_min": -10}, "plot": [["function(x){ return 2;}", [-10, 10], {}]]}
Parmi les fonctions suivantes, cocher celles qui sont paires.