Answer:
1.5
Step-by-step explanation:
From the given graph, we can observe below mentioned things.
- The graph of the function f(x) is a horizontal line passes through the point (0,1).
- The graph of the function g(x) passes through the points (0,-1) and (3,3)
Now, we find the equation of these two lines.
The equation of a horizontal line is in the form y = k, where k is constant and represents the y -coordinate of the point through which the line is passing.
Thus, the equation of f(x) is y = 1
Now, let the equation of g(x) be
g(x)=mx+b, where m is slope and b is y-intercept.
The y -intercept (where x =0) for g(x) is -1. Hence, b = -1
Therefore, the equation of g(x) is g(x)=mx-1
Now, it passes through the point (3,3)
3 = 3m-1
3m =4
m = 4/3
Thus, equation of g(x) is given by
[tex]g(x)=\frac{4}{3}x-1[/tex]
Now, for f(x) = g(x), we have
[tex]1=\frac{4}{3}x-1\\\\\frac{4}{3}x=2\\\\4x=6\\\\x=\frac{6}{4}\\\\x=1.5[/tex]
Thus, the input value is 1.5
