Question

Дана функция f(x)=a^x известно что f(1.5)=1\8. найдите f( -2)

Answer 1

$\displaystyle\bf\\f(x)=a^{x} \\\\f(1,5)=\frac{1}{8} \\\\\\\frac{1}{8} =a^{1,5} \\\\\\\Big(\frac{1}{8} \Big)^{2} =\Big(a^{1,5} \Big)^{2} \\\\\\a^{3} =\frac{1}{64} \\\\\\a^{3} =\Big(\frac{1}{4} \Big)^{3} \ \ \ \Rightarrow \ \ \ a=\frac{1}{4} \\\\\\f(x)=\Big(\frac{1}{4} \Big)^{x} \\\\\\f(-2)=\Big(\frac{1}{4} \Big)^{-2} =4^{2}=16\\\\\\Otvet \ : \ f(-2)=16$

Answer 2

$f(x) = {a }^{x} \\ f(1.5) = \frac{1}{8} \\ {a}^{1.5} = \frac{1}{8} \\ {a}^{ \frac{3}{2} } = \frac{1}{8} \\ ( {a}^{ \frac{3}{2} } ) {}^{2} = ( \frac{1}{8} ) {}^{2} \\ {a}^{3} = \frac{1}{64} \\ {a}^{3} = ( \frac{1}{4} ) {}^{3} \\ a = \frac{1}{4} \\ \\ f(x) = ( \frac{1}{4} ) {}^{x} \\ f( - 2) = ( \frac{1}{4} ) {}^{ - 2} = {4}^{2} = 16$