Answer:
f(g(x)) = -4
Explanation:
take 2 points in g(x)
(-6,0) (-4,-4)
g(x) = -2x - 12
g(-6) = -2(-6) - 12
g(-6) = 12 - 12 = 0
put 0 in x in f(x)
take 2 points in f(x)
(-4,0) (-2,-2)
f(x) = -x -4
f(0) = 0 - 4
f(0) = - 4
f(g(x)) = -4
showing the work below
Equation of a Line
(-6,0) (-4,-4)
To work with the two given points (-6,0) and (-4,-4), you can use the slope-intercept form of the equation of a line, which is y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope, you can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
So, substituting the given values, we get:
m = (-4 - 0) / (-4 - (-6))
m = -4 / 2
m = -2
To find the y-intercept, we can use one of the points and the slope in the slope-intercept form:
y = mx + b
0 = -2(-6) + b
0 = 12 + b
b = -12
Therefore, the equation of the line passing through the points (-6,0) and (-4,-4) is:
y = -2x - 12
(-4,0) (-2,-2)
To find the equation of the line passing through the two given points (-4,0) and (-2,-2), we can use the slope-intercept form of the equation of a line, which is y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Substituting the given values, we get:
m = (-2 - 0) / (-2 - (-4))
m = -2 / 2
m = -1
To find the y-intercept, we can use one of the points and the slope in the slope-intercept form:
y = mx + b
0 = -1(-4) + b
0 = 4 + b
b = -4
Therefore, the equation of the line passing through the points (-4,0) and (-2,-2) is:
y = -x - 4
ChatGPT