3a) The slope of the line parallel to y = -2x + 3 is ___ *
2 answers:
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Answer:
f^-1(x) = cuberoot(x+5)
see image
Step-by-step explanation:
To find an inverse function:
first, write y in place of f(x)
second, switch the x and y.
third, solve for y.
last, replace y with inverse function notation, f^-1(x)
see image.
Explanation
Problem #2
We must find the solution to the following system of inequalities:
(1) We solve for y the first inequality:
Now, we multiply both sides of the inequality by (-1), this changes the signs on both sides and inverts the inequality symbol:
The solution to this inequality is the set of all the points (x, y) over the line:
This line has:
• slope m = 3/2,
,• y-intercept b = -2.
(2) We solve for y the second inequality:
The solution to this inequality is the set of all the points (x, y) below the line:
This line has:
• slope m = -1/3,
,• y-intercept b = 2.
(3) Plotting the lines of points (1) and (2), and painting the region:
• over the line from point (1),
,• and below the line from point (2),
we get the following graph:
AnswerThe points that satisfy both inequalities are given by the intersection of the blue and red regions: