function

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Uchiha Sasuke
14/06 at 02:09
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Given two function \(f\left(x\right)=\sqrt{25x^2-30x+9}\), \(g\left(y\right)=y\). How many values of a are there such that \(f\left(a\right)=g\left(a\right)+7\)?

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Uchiha Sasuke
14/06 at 02:05
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Given two functions \(f\left(x\right)=5x+1\) and \(g\left(x\right)=ax+3\). Find the value of g(1) if \(a=f\left(2\right)-f\left(-1\right)\)

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Uchiha Sasuke
09/06/2019 at 02:55
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How many values of the whole number m such that the function \(y=\left(2016-m^2\right)x+3\) is increasing?
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    Tôn Thất Khắc Trịnh 13/06 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.