Найти область определения функции:
1.
[tex]y = \sqrt[10]{4 - log_{2}(x) } [/tex]
2.
[tex]y = \sqrt[8]{9 - {81}^{x - 1} } [/tex]
1.
[tex]y = \sqrt[10]{4 - log_{2}(x) } [/tex]
2.
[tex]y = \sqrt[8]{9 - {81}^{x - 1} } [/tex]
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1. y=¹⁰√(4-log₂(x))
ОДЗ:
x>0
4-log₂(x)≥0
log₂(x)≤4
log₂(x)≤log₂(16)
x≤16.
Ответ: x∈(0;16].
2. y=⁸√(9-81ˣ⁻¹)
9-81ˣ⁻¹≥0
81ˣ⁻¹≤9
9⁽²*⁽ˣ⁻¹⁾⁾≤9¹
9²ˣ⁻²≤9¹
2x-2≤1
2x≤3 |÷2
x≤3/2.
Ответ: x∈(-∞;3/2).