已知冪函數(shù)f(x)與指數(shù)函數(shù)g(x)都經(jīng)過點(diǎn)(3,1/27),求f(2)與g(-2)的值
已知冪函數(shù)f(x)與指數(shù)函數(shù)g(x)都經(jīng)過點(diǎn)(3,1/27),求f(2)與g(-2)的值
數(shù)學(xué)人氣：659 ℃時間：2020-04-15 02:25:51
優(yōu)質(zhì)解答
設(shè)f(x)=x^m,g(x)=a^xf(3)=3^m=1/27=3^(-3),所以m=-3,f(x)=x^(-3),f(2)=2^(-3)=1/8g(x)=a^3=1/27=(1/3)^3,所以a=1/3,g(x)=(1/3)^xg(-2)=(1/3)^(-2)=9.所以f(2)=1/8,g(-2)=9.
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