function
Uchiha Sasuke
14/06/2019 at 02:09-
Nguyễn Linh Chi 08/08/2019 at 09:44
\(f\left(a\right)=\sqrt{25a^2-30a+9}\)
\(g\left(a\right)=a\)
We have the following:
\(f\left(a\right)=g\left(a\right)+7\)
\(\Leftrightarrow\sqrt{25a^2-30a+9}=a+7\)
\(\Leftrightarrow\left\{{}\begin{matrix}25a^2-30a+9=\left(a+7\right)^2\\a+7\ge0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}a\ge-7\\24a^2-44a-40=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a\ge-7\\\left[{}\begin{matrix}a=\dfrac{5}{2}\\a=-\dfrac{2}{3}\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}a=\dfrac{5}{2}\\a=-\dfrac{2}{3}\end{matrix}\right.\)
Finally, there are two values of a.
Uchiha Sasuke selected this answer.
Uchiha Sasuke
14/06/2019 at 02:05-
Nguyễn Linh Chi 08/08/2019 at 10:01
We have: \(f\left(2\right)=5.2+1=11\)
\(f\left(-1\right)=5.\left(-1\right)+1=-4\)
then: \(a=f\left(2\right)-f\left(-1\right)=11-\left(-4\right)=15\)
Hence: \(g\left(1\right)=a.1+3=15.1+3=18\)
Uchiha Sasuke selected this answer.
Uchiha Sasuke
09/06/2019 at 02:55-
Tôn Thất Khắc Trịnh 13/06/2019 at 03:46
So as to have the function be increasing, 2016-m2 must be positive. Therefore, 2016 must be greater than m2. Since 2016 is a positive number, m has to range from \(-\sqrt{2016}\) to \(\sqrt{2016}\). In other words, m has to be between -44.899 and 44.899. Since m is a whole number, the minimal value of m is -44 and the maximum is 44. To calculate the number of values, we use this formula:
\(N=\frac{44-(-44)}{1}+1=89\)To conclude, there are 89 values of m such that the function is increasing.
Uchiha Sasuke selected this answer.