The inverse function theorem says
![\dfrac{\mathrm df^{-1}}{\mathrm dx}(16)=\dfrac1{\frac{\mathrm df}{\mathrm dx}(f^{-1}(16))}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20df%5E%7B-1%7D%7D%7B%5Cmathrm%20dx%7D%2816%29%3D%5Cdfrac1%7B%5Cfrac%7B%5Cmathrm%20df%7D%7B%5Cmathrm%20dx%7D%28f%5E%7B-1%7D%2816%29%29%7D)
We have
![f(x)=x^2+4x-5](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2%2B4x-5)
defined on
, for which we get
![f^{-1}(x)=-2+\sqrt{x+9}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D-2%2B%5Csqrt%7Bx%2B9%7D)
and
![f^{-1}(16)=-2+\sqrt{16+9}=3](https://tex.z-dn.net/?f=f%5E%7B-1%7D%2816%29%3D-2%2B%5Csqrt%7B16%2B9%7D%3D3)
The derivative of
is
![f'(x)=2x+4](https://tex.z-dn.net/?f=f%27%28x%29%3D2x%2B4)
So we end up with
![\dfrac{\mathrm df^{-1}}{\mathrm dx}(16)=\dfrac1{\frac{\mathrm df}{\mathrm dx}(3)}=\dfrac1{10}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20df%5E%7B-1%7D%7D%7B%5Cmathrm%20dx%7D%2816%29%3D%5Cdfrac1%7B%5Cfrac%7B%5Cmathrm%20df%7D%7B%5Cmathrm%20dx%7D%283%29%7D%3D%5Cdfrac1%7B10%7D)
Answer:
8
Step-by-step explanation:
4 different shirts would be 4 combinations. You can have one of each of the jeans on the mannequin, giving 4x2=8.
Answer: 19
Step by step:
15-(-4)
Negative* negative= positive
So.. negative 1 times -4=4
15+4= 19
Answer:
Step-by-step explanation:
SOH CAH TOA to help remember how the trig functions fit on the triangle
use SOH since we know the angle and the hypotenuse and want to find the opposite side
Sin(x)= Opp/ Hyp
Hyp* sin(38) = Opp
12* 0.6156614753 = Opp
7.3879377...
7.4 is the answer
Answer: 23
Explanation:
Second quartile is another word for the median