a) Ta có:
\(f\left( {\dfrac{1}{5}} \right) = \dfrac{5}{{4.\dfrac{1}{5}}} = \dfrac{5}{{\dfrac{4}{5}}} = 5:\dfrac{4}{5} = 5.\dfrac{5}{4} = \dfrac{{25}}{4};\)
\(f\left( { - 5} \right) = \dfrac{5}{{4.\left( { - 5} \right)}} = \dfrac{5}{{ - 20}} = \dfrac{{ - 1}}{4};\)
\(f\left( {\dfrac{4}{5}} \right) = \dfrac{5}{{4.\dfrac{4}{5}}} = \dfrac{5}{{\dfrac{{16}}{5}}} = 5:\dfrac{{16}}{5} = 5.\dfrac{5}{{16}} = \dfrac{{25}}{{16}}\)
b) Ta có:
\(f\left( { - 3} \right) = \dfrac{5}{{4.\left( { - 3} \right)}} = \dfrac{5}{{ - 12}} = \dfrac{{ - 5}}{{12}};\)
\(f\left( { - 2} \right) = \dfrac{5}{{4.\left( { - 2} \right)}} = \dfrac{5}{{ - 8}} = \dfrac{{ - 5}}{8};\)
\(f\left( { - 1} \right) = \dfrac{5}{{4.\left( { - 1} \right)}} = \dfrac{5}{{ - 4}} = \dfrac{{ - 5}}{4};\)
\(f\left( { - \dfrac{1}{2}} \right) = \dfrac{5}{{4.\left( { - \dfrac{1}{2}} \right)}} = \dfrac{5}{{\dfrac{{ - 4}}{2}}} = \dfrac{5}{{ - 2}} = \dfrac{{ - 5}}{2}\);
\(f\left( {\dfrac{1}{4}} \right) = \dfrac{5}{{4.\dfrac{1}{4}}} = \dfrac{5}{{\dfrac{4}{4}}} = \dfrac{5}{1} = 5\);
\(f\left( 1 \right) = \dfrac{5}{{4.1}} = \dfrac{5}{4}\);
\(f\left( 2 \right) = \dfrac{5}{{4.2}} = \dfrac{5}{8}\)
Ta có bảng sau:
\(x\) | –3 | –2 | –1 | \( - \dfrac{1}{2}\) | \(\dfrac{1}{4}\) | 1 | 2 |
\(y = f\left( x \right) = \dfrac{5}{{4x}}\) | \(\dfrac{{ - 5}}{{12}}\) | \(\dfrac{{ - 5}}{8}\) | \(\dfrac{{ - 5}}{4}\) | \(\dfrac{{ - 5}}{2}\) | 5 | \(\dfrac{5}{4}\) | \(\dfrac{5}{8}\) |