6.1-bo'lim : Eksponensial funksiyalar
1. \(f\left( x \right) = {4^x}\) funksiyasini hisobga olgan holda quyidagi har birini baholang.
- \(f\left( { - 2} \right)\)
- \(f\left( {\displaystyle - \frac{1}{2}} \right)\)
- \(f\left( 0 \right)\)
- \(f\left( 1 \right)\)
- \(f\left( {\displaystyle \frac{3}{2}} \right)\)
a \(f\left( { - 2} \right)\) Yechim
Bu erda qilishimiz kerak bo'lgan yagona narsa \(x\) ni ulash va har qanday tez arifmetikani bajarishdir.
\[f\left( { - 2} \right) = {4^{ - 2}} = \frac{1}{{{4^2}}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{1}{{16}}}}\]b \(f\left( {\displaystyle - \frac{1}{2}} \right)\) Yechim
Bu erda qilishimiz kerak bo'lgan yagona narsa \(x\) ni ulash va har qanday tez arifmetikani bajarishdir.
\[f\left( { - \frac{1}{2}} \right) = {4^{ - \,\,\frac{1}{2}}} = \frac{1}{{{4^{\frac{1}{2}}}}} = \frac{1}{{\sqrt 4 }} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{1}{2}}}\]c \(f\left( 0 \right)\) Yechim
Bu erda qilishimiz kerak bo'lgan yagona narsa \(x\) ni ulash va har qanday tez arifmetikani bajarishdir.
\[f\left( 0 \right) = {4^0} = \require{bbox} \bbox[2pt,border:1px solid black]{1}\]d \(f\left( 1 \right)\) Yechim
Bu erda qilishimiz kerak bo'lgan yagona narsa \(x\) ni ulash va har qanday tez arifmetikani bajarishdir.
\[f\left( 1 \right) = {4^1} = \require{bbox} \bbox[2pt,border:1px solid black]{4}\]e \(f\left( {\displaystyle \frac{3}{2}} \right)\) Yechim
Bu erda qilishimiz kerak bo'lgan yagona narsa \(x\) ni ulash va har qanday tez arifmetikani bajarishdir.
\[f\left( {\frac{3}{2}} \right) = {4^{\,\frac{3}{2}}} = {\left( {{4^{\frac{1}{2}}}} \right)^3} = {2^3} = \require{bbox} \bbox[2pt,border:1px solid black]{8}\]