The two functions f(x) and g(x) are linear. So, the input value for which [tex]f(x)=g(x)[/tex] is [tex]x=-1[/tex]. Ans the common point will be (-1,3).
From the given table, the function f(x) passes through the points (-2,3), (-1,3) and (0,3). The function g(x) passes through the points (-2,4), (-1,3) and (0,2).
It is also given that the functions are linear. So, they will form a line on the graph.
Now, the two point form of a line is written as,
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the point through which the line is passing.
So, the expression for f(x) can be written as,
[tex]y-3=\dfrac{3-3}{-1-(-2)}(x-(-2))\\y-3=0\\f(x)=3[/tex]
Also, the expression for g(x) can be written as,
[tex]y-4=\dfrac{3-4}{-1-(-2)}(x-(-2))\\y-4=\dfrac{-1}{1}(x+2)\\y-4=-x-2\\g(x)=2-x[/tex]
It is required to get the value of x such that f(x) becomes equal to g(x).
So, the such common value of x will be,
[tex]f(x)=g(x)\\3=2-x\\x=-1[/tex]
Thus, the input value for which [tex]f(x)=g(x)[/tex] is [tex]x=-1[/tex].
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https://brainly.com/question/4441465
