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)
For 2 it is slope 3 and y intercept (0,5)
For 3 it is slope y=-4x-5
From the Formula:
Distance = Sqr Root [ (x2- x1)^2 + (y2 - y1)^2 ]
Distance = Sqr Root [ (20 --15)^2 + 18 -18)^2 ]
Distance = Sqr Root [ 1,225 + 0]
Distance = 35
Answer:
The expression representing Noah’s new number is 
Step-by-step explanation:
Noah started with a number, x.
Four times the number x is 4x
The difference of four times the number and three is 4x - 3
The difference of four times the number and three cubed is 
Thus, the expression representing Noah’s new number is
