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)
Answer:
16 and 82 degrees
Step-by-step explanation:
You can sum all of the angles together and solve for x.
(x - 1) + (5x - 3) + (5x - 3) = 180
11x - 7 = 180
11x = 187
x = 17
The first angle is 16 degrees. (17 - 1)
The other two angles are 82 degrees(5(17) - 3)
Answer:
x = 17
y = 17
Step-by-step explanation:
You would need to use the following trigonometric functions cosine and sin. Sin is used for the y-variable to get the answer and cosine is used for the x-variable to get the answer. For this case, you would need to do 34 sin 30 for y and 34 cos 30 for x. You should get 17 for y and 17 root 3 for x when you put it in the calculator.
Answer:
65kg
Step-by-step explanation: