Note that f(x) as given is <em>not</em> invertible. By definition of inverse function,
which is a cubic polynomial in with three distinct roots, so we could have three possible inverses, each valid over a subset of the domain of f(x).
Choose one of these inverses by restricting the domain of f(x) accordingly. Since a polynomial is monotonic between its extrema, we can determine where f(x) has its critical/turning points, then split the real line at these points.
f'(x) = 3x² - 1 = 0 ⇒ x = ±1/√3
So, we have three subsets over which f(x) can be considered invertible.
• (-∞, -1/√3)
• (-1/√3, 1/√3)
• (1/√3, ∞)
By the inverse function theorem,
where f(a) = b.
Solve f(x) = 2 for x :
x³ - x + 2 = 2
x³ - x = 0
x (x² - 1) = 0
x (x - 1) (x + 1) = 0
x = 0 or x = 1 or x = -1
Then can be one of
• 1/f'(-1) = 1/2, if we restrict to (-∞, -1/√3);
• 1/f'(0) = -1, if we restrict to (-1/√3, 1/√3); or
• 1/f'(1) = 1/2, if we restrict to (1/√3, ∞)
-2 and 8
Im not sure if you have options to choose for but i'm like 95% sure that answer is correct.
Your slope would be -1/4x. If you look at the y-intercept on your graph, which is -2, you would start to count up one box and over 4 boxes to the left. We call this rise/run. So knowing what the slope is now, your entire equation would be y= -1/4x - 2. (Also, if the line is going up towards the left it is a negative slope, if it's to the right it is positive.) I hope this helps love! :)
Answer:
1,298
Step-by-step explanation:
Step 1:
1,278 + 20
Answer:
1,298
Hope This Helps :)
Answer: B. perpendicular lines because they intersect at a right angle, making them perpendicular.