parity 1.1^x+9^xdx

{ "query": { "display": "parity $$1.1^{x}+9^{x}dx$$", "symbolab_question": "FUNCTION#parity 1.1^{x}+9^{x}dx" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Functions", "subTopic": "parity", "default": "\\mathrm{Neither\\:even\\:nor\\:odd}", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Parity of $$1.1^{x}+9^{x}dx:{\\quad}$$Neither even nor odd", "steps": [ { "type": "definition", "title": "Parity Definition", "text": "Even Function: A function is even if $$f\\left(-x\\right)=f\\left(x\\right)$$ for all $$x\\in\\mathbb{R}$$<br/>Odd Function: A function is odd if $$f\\left(-x\\right)=-f\\left(x\\right)$$ for all $$x\\in\\mathbb{R}$$" }, { "type": "interim", "title": "$$f\\left(-x\\right):{\\quad}1.1^{-x}+9^{-x}d-x$$", "steps": [ { "type": "step", "primary": "Plug $$-x\\:$$into $$1.1^{x}+9^{x}dx$$", "result": "=1.1^{-x}+9^{-x}d\\left(-x\\right)" }, { "type": "step", "primary": "Remove parentheses: $$\\left(-a\\right)=-a$$", "result": "=1.1^{-x}+9^{-x}d-x" } ], "meta": { "interimType": "N/A" } }, { "type": "interim", "title": "$$-f\\left(x\\right):{\\quad}-1.1^{x}-9^{x}dx$$", "steps": [ { "type": "step", "primary": "Negate $$1.1^{x}+9^{x}dx$$", "result": "=-\\left(1.1^{x}+9^{x}dx\\right)" }, { "type": "step", "primary": "Distribute parentheses", "result": "=-\\left(1.1^{x}\\right)-\\left(9^{x}dx\\right)" }, { "type": "step", "primary": "Apply minus-plus rules", "secondary": [ "$$+\\left(-a\\right)=-a$$" ], "result": "=-1.1^{x}-9^{x}dx" } ], "meta": { "interimType": "N/A" } }, { "type": "step", "primary": "Check parity of $$1.1^{x}+9^{x}dx$$" }, { "type": "interim", "title": "Check if Even:$${\\quad}$$False", "steps": [ { "type": "step", "result": "f\\left(x\\right)=1.1^{x}+9^{x}dx,\\:f\\left(-x\\right)=1.1^{-x}+9^{-x}d-x" }, { "type": "step", "result": "f\\left(x\\right)\\ne\\:f\\left(-x\\right)" }, { "type": "step", "primary": "Therefore", "result": "1.1^{x}+9^{x}dx\\mathrm{\\:is\\:not\\:an\\:even\\:function}" } ], "meta": { "interimType": "Parity Check Even Title 0Eq" } }, { "type": "interim", "title": "Check if Odd:$${\\quad}$$False", "steps": [ { "type": "step", "result": "-f\\left(x\\right)=-1.1^{x}-9^{x}dx,\\:f\\left(-x\\right)=1.1^{-x}+9^{-x}d-x" }, { "type": "step", "result": "-f\\left(x\\right)\\ne\\:f\\left(-x\\right)" }, { "type": "step", "primary": "Therefore", "result": "1.1^{x}+9^{x}dx\\mathrm{\\:is\\:not\\:an\\:odd\\:function}" } ], "meta": { "interimType": "Parity Check Odd Title 0Eq" } }, { "type": "step", "result": "\\mathrm{Neither\\:even\\:nor\\:odd}" } ], "meta": { "solvingClass": "Function Parity" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "1.1^{x}+9^{x}dx" }, "showViewLarger": true } }, "meta": { "showVerify": true } }