Answer:
(f⁻¹)'(b) = 1/f'(f⁻¹(b)) = 1/f'(a)
Step-by-step explanation:
The function f⁻¹(x) is the reflection of the function f(x) across the line y=x. Every point (a, b) that is on the graph of f(x) is reflected to be a point (b, a) on the graph of f⁻¹(x).
Any line with slope m reflected across the line y=x will have slope 1/m. (x and y are interchanged, so m=∆y/∆x becomes ∆x/∆y=1/m) Since f'(x) is the slope of the tangent line at (x, f(x)), 1/f'(x) will be the slope of the tangent line at (f(x), x).
Replacing x with f⁻¹(x) in the above relation, you get ...
... (f⁻¹)'(x) = 1/f'(f⁻¹(x)) will be the slope at (x, f⁻¹(x))
Putting your given values in this relation, you get
... (f⁻¹)'(b) = 1/f'(f⁻¹(b)) = 1/f'(a)
It's A. First of all, one of the only 2 things in math that will NEVER be negative is distances/lengths and times. You have a distance here, so because one of your 2 numbers is negative, you have to take the absolute value of the difference. -8-5 = -11, but the absolute value of that is 11. Put the numbers on a number line and count the units between -8 and +5 and there are 11 units between those 2 numbers.
The numbers before the X are the slope, the numbers after the x are the Y- intercepts.
1. Slope = -3
2. y-intercept = -8
3. Slope = 5/4, y-intercept = 9
4. 8x+6y =12
subtract 8x from each side to get Y on the left side:
6y = -8x +12
Divide each term by 6:
y = -8x /6 + 12/6
y = -4/3x + 2
The answer is A.
5. Rewrite the equation in slope intercept form:
x-3y = -3
-3y = -x -3
y = 1/3x +1
The slope is 1/3, the y-intercept is 1
The correct line is B. line b