Hướng dẫn giải Bài 7 (Trang 143 SGK Toán Đại số & Giải tích 11)

<p>Xét tính liên tục trên R của hàm số:</p> <div class="ads_ads ads_1"><img src="https://vietjack.com/giai-toan-lop-11/images/bai-7-trang-143-sgk-dai-so-11-2.PNG" alt="Giải bài 7 trang 143 sgk Đại Số 11 | Để học tốt Toán 11" /></div> <div class="ads_ads ads_1"><strong>Giải:</strong></div> <div class="ads_ads ads_1">Tập xác đinh D= R</div> <div class="ads_ads ads_1">Hàm số y = g(x) liên tục trên các khoảng <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mo>∞</mo><mo>;</mo><mo> </mo><mn>2</mn></mrow></mfenced><mo> </mo><mi>v</mi><mi>à</mi><mo> </mo><mfenced><mrow><mn>2</mn><mo> </mo><mo>;</mo><mo>+</mo><mo>∞</mo></mrow></mfenced></math></div> <div class="ads_ads ads_1">Tại <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>0</mn></msub><mo>=</mo><mn>2</mn></math> ta có g(2) =3</div> <div class="ads_ads ads_1"><math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mrow><mi>l</mi><mi>i</mi><mi>m</mi><mo> </mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mrow><mi>x</mi><mo>→</mo><mn>2</mn><mo>-</mo></mrow></munder><mo>=</mo><munder><mrow><mi>l</mi><mi>i</mi><mi>m</mi><mo> </mo><mo>(</mo><mn>5</mn><mo>-</mo><mi>x</mi><mo>)</mo><mo> </mo><mo>=</mo><mn>3</mn></mrow><mrow><mi>x</mi><mo>→</mo><mn>2</mn><mo>-</mo></mrow></munder></math></div> <div class="ads_ads ads_1"><math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mrow><mi>l</mi><mi>i</mi><mi>m</mi><mo> </mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mrow><mi>x</mi><mo>→</mo><mn>2</mn><mo>+</mo></mrow></munder><mo> </mo><mo>=</mo><munder><mrow><mi>l</mi><mi>i</mi><mi>m</mi></mrow><mrow><mi>x</mi><mo>→</mo><mn>2</mn><mo>+</mo></mrow></munder><mfrac><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi><mo>-</mo><mn>2</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfrac><mo>=</mo><munder><mrow><mi>l</mi><mi>i</mi><mi>m</mi></mrow><mrow><mi>x</mi><mo>→</mo><mn>2</mn><mo>+</mo></mrow></munder><mfrac><mrow><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfrac><mo> </mo><mo>=</mo><munder><mrow><mi>l</mi><mi>i</mi><mi>m</mi></mrow><mrow><mi>x</mi><mo>→</mo><mn>2</mn><mo>+</mo></mrow></munder><mfenced><mrow><mi>x</mi><mo>=</mo><mn>1</mn></mrow></mfenced><mo>=</mo><mn>3</mn></math></div> <div class="ads_ads ads_1">Vậy <math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mrow><mi>l</mi><mi>i</mi><mi>m</mi></mrow><mrow><mi>x</mi><mo>→</mo><mn>2</mn><mo>-</mo></mrow></munder><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><munder><mrow><mi>l</mi><mi>i</mi><mi>m</mi></mrow><mrow><mi>x</mi><mo>→</mo><mn>2</mn><mo>+</mo></mrow></munder><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>= g(2) nên g(x) liên tục tai x=2</div> <div class="ads_ads ads_1">Vậy y= g(x) liên tục trên R</div>