Hướng dẫn Giải Bài 14 (trang 48, SGK Toán 9, Tập 1)

Hướng dẫn giải Bài 14 (Trang 48 SGK Toán 9, Tập 1)

Bài 14 (Trang 48 SGK Toán 9, Tập 1): Hàm số bậc nhất <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><mfenced><mrow><mn>1</mn><mo> </mo><mo>-</mo><mo> </mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mi>x</mi><mo> </mo><mo>-</mo><mo> </mo><mn>1</mn></math> a) Hàm số trên là đồng biến hay nghịch biến trên R? Vì sao? b) Tính giá trị của y khi <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mn>1</mn><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>5</mn></msqrt></math> c) Tính giá trị của x khi <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>5</mn></msqrt></math>.   Hướng dẫn giải: a) Ta có <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo> </mo><mo>=</mo><mo> </mo><mn>1</mn><mo> </mo><mo>-</mo><mo> </mo><msqrt><mn>5</mn></msqrt><mo> </mo><mo><</mo><mo> </mo><mn>0</mn></math> nên hàm số đã cho nghịch biến trên R. b) Thay <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mn>1</mn><mo> </mo><mo>-</mo><mo> </mo><msqrt><mn>5</mn></msqrt></math> vào hàm số, ta có: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><mfenced><mrow><mn>1</mn><mo>-</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><mn>1</mn><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mo> </mo><mo>-</mo><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mn>1</mn><mo> </mo><mo>-</mo><mo> </mo><mn>5</mn><mo> </mo><mo>-</mo><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mn>5</mn></math> c) Khi <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>5</mn></msqrt></math>, ta có: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>5</mn></msqrt><mo> </mo><mo>=</mo><mo> </mo><mfenced><mrow><mn>1</mn><mo> </mo><mo>-</mo><mo> </mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mi>x</mi><mo> </mo><mo>-</mo><mo> </mo><mn>1</mn><mspace linebreak="newline"/><mspace linebreak="newline"/><mo> </mo><mo>⇔</mo><mo> </mo><msqrt><mn>5</mn></msqrt><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mfenced><mrow><mn>1</mn><mo> </mo><mo>-</mo><mo> </mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mi>x</mi><mspace linebreak="newline"/><mspace linebreak="newline"/><mo> </mo><mo>⇔</mo><mo> </mo><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>1</mn><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>5</mn></msqrt></mrow><mrow><mn>1</mn><mo> </mo><mo>-</mo><mo> </mo><msqrt><mn>5</mn></msqrt></mrow></mfrac><mspace linebreak="newline"/><mspace linebreak="newline"/><mo> </mo><mo>⇔</mo><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mfenced><mrow><mn>1</mn><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><mn>1</mn><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>5</mn></msqrt></mrow></mfenced></mrow><mrow><mn>1</mn><mo> </mo><mo>-</mo><mo> </mo><mn>5</mn></mrow></mfrac><mspace linebreak="newline"/><mspace linebreak="newline"/><mo> </mo><mo>⇔</mo><mo> </mo><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>1</mn><mo> </mo><mo>+</mo><mo> </mo><mn>2</mn><msqrt><mn>5</mn></msqrt><mo> </mo><mo>+</mo><mo> </mo><mn>5</mn></mrow><mrow><mo>-</mo><mn>4</mn></mrow></mfrac><mspace linebreak="newline"/><mspace linebreak="newline"/><mo> </mo><mo>⇔</mo><mo> </mo><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>6</mn><mo> </mo><mo>+</mo><mo> </mo><mn>2</mn><msqrt><mn>5</mn></msqrt></mrow><mrow><mo>-</mo><mn>4</mn></mrow></mfrac><mspace linebreak="newline"/><mspace linebreak="newline"/><mo> </mo><mo>⇔</mo><mo> </mo><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mfrac><mrow><mn>3</mn><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>5</mn></msqrt></mrow><mn>2</mn></mfrac></math> Vậy với <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>5</mn></msqrt><mo> </mo><mi>t</mi><mi>h</mi><mi>ì</mi><mo> </mo><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mfrac><mrow><mn>3</mn><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>5</mn></msqrt></mrow><mn>2</mn></mfrac></math>.