Question

Consider the functions shown on the graph. What is the input value for which the statement f(x) = g(x) is true?

Answer 1

The answer is a=1.5 hope I was able to help

Answer 2

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

$g(x)=\frac{4}{3}x-1$

Now, for f(x) = g(x), we have

$1=\frac{4}{3}x-1\\\\\frac{4}{3}x=2\\\\4x=6\\\\x=\frac{6}{4}\\\\x=1.5$

Thus, the input value is 1.5