3 years ago

Determine whether if the function is one to one. If so find its inverse

1 answer:

7 0

A one-to-one function, has a one to one relation obviously, meaning for every x-coordinate, there's a unique y-coordinate value, so the pairs never really repeat, let's check this one,

$\bf \{(-1,\stackrel{y-re peat}{1}),(-3,-2),(0,\stackrel{y-re peat}{1}),(4,2)\}\impliedby 
\begin{array}{llll}
\textit{therefore is not a}\\
\textit{ \underline{one-to-one}}
\end{array}$

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Given the sequence in the table below, determine the sigma notation of the sum for term 4 through term 15.

Naya [18.7K]

It's a geometric sequence.

$4,-12,36,... \\ \\
a_1=4 \\
r=\frac{a_2}{a_1}=\frac{-12}{4}=-3 \\ \\
a_n=a_1 \times r^{n-1} \\
a_n=4 \times (-3)^{n-1} \\
a_n=4 \times (-3)^{-1} \times (-3)^n \\
a_n=4 \times (-\frac{1}{3}) \times (-3)^n \\
a_n=-\frac{4}{3}(-3)^n$

It's the sum for term 4 through term 15.

$\boxed{ \sum\limits_{n=4}^{15} (\frac{4}{3}(-3)^n)}$