若函數(shù)f(x)的圖象經(jīng)過點(diǎn)(0,-1)則函數(shù)f(x+4)的反函數(shù)的圖象必經(jīng)過點(diǎn)________.
(-1,-4)
分析:利用在函數(shù)值-1保持不變的情況下,求出與原函數(shù)自變量x=0與之對應(yīng)的復(fù)合函數(shù)的自變量x=-4,由函數(shù)與反函數(shù)定義域和值域的關(guān)系得出反函數(shù)圖象經(jīng)過點(diǎn)(-1,-4).
解答:由函數(shù)y=f(x)的圖象經(jīng)過點(diǎn)(0,-1),得f(0)=-1,
所以當(dāng)x=-4時(shí)有f(4+x)=f(0)=-1,
從而函數(shù)y=f(4+x)過點(diǎn)(-4,-1),則函數(shù)y=f(4+x)的反函數(shù)并經(jīng)過點(diǎn)(-1,-4),
故答案為:(-1,-4).
點(diǎn)評:本題主要考查復(fù)合函數(shù)與原函數(shù)關(guān)系,以及函數(shù)與反函數(shù)關(guān)系,屬于基礎(chǔ)題.