MATH SOLVE

2 months ago

Q:
# The table shows some values of f(x) and g(x) for different values of x:Complete the chart and determine the solution of the equation f(x) = g(x).A.x=-1B.x=0C.x=2D.x=25the table picture is on top please help

Accepted Solution

A:

Answer:C. x=2Step-by-step explanation:To complete the table, let's plug in the x-values into [tex]f(x)[/tex] and [tex]g(x)[/tex], so:For [tex]f(x)[/tex]:[tex]If \ x=0: \\ \\ f(0)=9(0)+7=7 \\ \\ \\ If \ x=1: \\ \\ f(1)=9(1)+7=16 \\ \\ \\ If \ x=2: \\ \\ f(2)=9(2)+7=25[/tex]For [tex]g(x)[/tex]:[tex]If \ x=-2: \\ \\ g(-2)=5^{-2}=0.04 \\ \\ \\ If \ x=-1: \\ \\ g(-1)=5^{-1}=0.2 \\ \\ \\ If \ x=2: \\ \\ g(2)=5^{2}=25[/tex]From this, the complete table is:[tex]\left|\begin{array}{c|c|c}x & f(x)=9x+7 & g(x)=5^{x}\\-2 & -11 & 0.04\\-1 & -2 & 0.2\\0 & 7 & 1\\1 & 16 & 5\\2 & 25 & 25\end{array}\right|[/tex]From the table, you can see that [tex]f(x)=g(x)=25[/tex] when [tex]x=2[/tex] so the correct option is C. x=2. But what does [tex]x=2[/tex] mean? It means that at this x-value, the graph of the linear function [tex]f(x)[/tex] and the graph of the exponential function [tex]g(x)[/tex] intersect and the point of intersection is [tex](2,25)[/tex]