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let g(x)=log_2x1. find g(5)2. find g(-3)3. find g^-1(x)4. find g^-1(-3)

Let Gxlog2x1 Find G52 Find G33 Find G1x4 Find G13 class=

Sagot :

[tex]g(x)=\log _2x[/tex]

You evaluate the equation in the given values of x:

[tex]\log _ba=\frac{\log a}{\log b}[/tex]

1. g(5)[tex]\begin{gathered} g(5)=\log _25 \\ g(5)=\frac{\log 5}{\log 2}=2.321 \end{gathered}[/tex][tex]g(5)=2.321[/tex]2. g(-3)[tex]\begin{gathered} g(-3)=\log _2(-3) \\ g(-3)=\frac{\log (-3)}{\log 2}=\text{undefined} \end{gathered}[/tex]

The logarithm of a negative number is undefined

3. g^-1(x)

To find the inverse function you:

-write the function with x and y:

[tex]\begin{gathered} g(x)=\log _2x \\ y=\log _2x \end{gathered}[/tex]

-Solve variable x:

knowing that:

[tex]\begin{gathered} \log _ba=c \\ b^c=a \end{gathered}[/tex][tex]\begin{gathered} y=\log _2x \\ \\ 2^y=x \end{gathered}[/tex]

- Change the x for (g^-1(x)) and the y for x:

[tex]g^{-1}(x)=2^x[/tex]4.g^-1(-3)​

As:

[tex]n^{-m}=\frac{1}{n^m}[/tex]

[tex]\begin{gathered} g^{-1}(-3)=2^{-3} \\ \\ =\frac{1}{2^3}=\frac{1}{8} \end{gathered}[/tex]

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