https://peda.net/id/06378b7c391 2020-01-17T13:32:20+02:00 https://peda.net/:static/537/peda.net.logo.bg.svg <div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div> https://peda.net/id/327cae5e3c1 2020-01-21T09:03:59+02:00 <div>a)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B2x-1%7D%3D4" alt="\sqrt{2x-1}=4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D8%7B%2C%7D5" alt="x=8{,}5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B2%5Cleft(8%7B%2C%7D5%5Cright)-1%7D%3D4" alt="\sqrt{2\left(8{,}5\right)-1}=4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B17-1%7D%3D4" alt="\sqrt{17-1}=4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B16%7D%3D4" alt="\sqrt{16}=4"/></div> <div>b)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%5B3%5D%7B1-x%7D%3D-2" alt="\sqrt[3]{1-x}=-2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D9" alt="x=9"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%5B3%5D%7B1-9%7D%3D-2" alt="\sqrt[3]{1-9}=-2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%5B3%5D%7B-8%7D%3D-2" alt="\sqrt[3]{-8}=-2"/></div> <div>c)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7Bx%5E2-2x-2%7D%3D1" alt="\sqrt{x^2-2x-2}=1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(%5Csqrt%7Bx%5E2-2x-2%7D%5Cright)%5E2%3D1%5E2" alt="\left(\sqrt{x^2-2x-2}\right)^2=1^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-2x-2%3D1" alt="x^2-2x-2=1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D-1%5C%20tai%5C%20x%3D3" alt="x=-1\ tai\ x=3"/></div> 2020-01-21T09:03:59+02:00 https://peda.net/id/ea9880503c1 2020-01-21T08:54:49+02:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D%5Csqrt%7B-2x%2B7%7D%7B%2C%7D%5C%20x%3E3%7B%2C%7D5" alt="f\left(x\right)=\sqrt{-2x+7}{,}\ x&gt;3{,}5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(-1%5Cright)%3D%5Csqrt%7B-2%5Cleft(-1%5Cright)%2B7%7D%3D%5Csqrt%7B9%7D%3D3" alt="f\left(-1\right)=\sqrt{-2\left(-1\right)+7}=\sqrt{9}=3"/><img src="https://i.imgur.com/b231pun.png" alt=""/><br/> <br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D%5Csqrt%5B3%5D%7B3x-5%7D" alt="f\left(x\right)=\sqrt[3]{3x-5}"/><br/> <div>funktio on määritelty kaikilla x arvoilla</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(-1%5Cright)%3D%5Csqrt%5B3%5D%7B3%5Cleft(-1%5Cright)-5%7D%3D%5Csqrt%5B3%5D%7B-3-5%7D%3D%5Csqrt%5B3%5D%7B-8%7D%3D-2" alt="f\left(-1\right)=\sqrt[3]{3\left(-1\right)-5}=\sqrt[3]{-3-5}=\sqrt[3]{-8}=-2"/><img src="https://i.imgur.com/Zy2Tahu.png" alt=""/><br/> <br/> </div> 2020-01-21T08:54:49+02:00 https://peda.net/id/d747e38e3c1 2020-01-21T08:47:07+02:00 a)<br/> <img src="https://i.imgur.com/XtHQGmF.png" alt=""/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B7-x%7D%3Dx-1" alt="\sqrt{7-x}=x-1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(%5Csqrt%7B7-x%7D%5Cright)%5E2%3D%5Cleft(x-1%5Cright)%5E2" alt="\left(\sqrt{7-x}\right)^2=\left(x-1\right)^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=7-x%3D%5Cleft(x-1%5Cright)%5E2" alt="7-x=\left(x-1\right)^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D3" alt="x=3"/><br/> 2020-01-21T08:47:07+02:00 https://peda.net/id/8cbe46743c1 2020-01-21T08:37:52+02:00 a)<br/> funktio on määritelty x:n arvoilla x&lt;4, sillä<br/> mikä tahansa neljää suurempi arvo saisi neliöjuuren sisälle negatiivisen luvun<br/> nollakohdat:<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=1-%5Csqrt%7B4-x%7D%3D0" alt="1-\sqrt{4-x}=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=1%3D%5Csqrt%7B4-x%7D" alt="1=\sqrt{4-x}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=1%5E2%3D%5Cleft(%5Csqrt%7B4-x%7D%5Cright)%5E2" alt="1^2=\left(\sqrt{4-x}\right)^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=1%3D4-x" alt="1=4-x"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D3" alt="x=3"/><br/> b)<br/> funktion arvo kohdassa -5:<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(-5%5Cright)%3D1-%5Csqrt%7B4-%5Cleft(-5%5Cright)%7D" alt="f\left(-5\right)=1-\sqrt{4-\left(-5\right)}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(-5%5Cright)%3D1-%5Csqrt%7B9%7D" alt="f\left(-5\right)=1-\sqrt{9}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(-5%5Cright)%3D-2" alt="f\left(-5\right)=-2"/><br/> missä kohdassa funktio saa arvon -5<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D-5" alt="f\left(x\right)=-5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=1-%5Csqrt%7B4-x%7D%3D-5" alt="1-\sqrt{4-x}=-5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=6%5E2%3D%5Cleft(%5Csqrt%7B4-x%7D%5Cright)%5E2" alt="6^2=\left(\sqrt{4-x}\right)^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=36%3D4-x" alt="36=4-x"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D-32" alt="x=-32"/><!--filtered attribute: style="display: inline;"--> 2020-01-21T08:37:52+02:00 https://peda.net/id/53ca34c83c1 2020-01-21T08:29:07+02:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=7-x" alt="7-x"/><br/> b)<br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=h%5E2%3Dx%5E2%2B%5Cleft(7-x%5Cright)%5E2" alt="h^2=x^2+\left(7-x\right)^2"/></div> <div>c)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=5%5E2%3Dx%5E2%2B%5Cleft(7-x%5Cright)%5E2" alt="5^2=x^2+\left(7-x\right)^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D3%5C%20tai%5C%20x%3D4" alt="x=3\ tai\ x=4"/></div> 2020-01-21T08:29:07+02:00 https://peda.net/id/f7fc9e52392 2020-01-17T14:14:54+02:00 <p>A3<br/> B1<br/> C13<br/> D1<br/> E1</p> 2020-01-17T14:14:54+02:00 https://peda.net/id/b7cbd866392 2020-01-17T14:13:06+02:00 a) 2,6<br/> b) 2,3 2020-01-17T14:13:06+02:00 https://peda.net/id/50eab31a392 2020-01-17T14:10:13+02:00 <p>A2<br/> B1<br/> C4<br/> D3<br/> <br/> </p> 2020-01-17T14:10:13+02:00