Answer: x(x−6)
Step-by-step explanation:
True they could be congruent by ASA
Answer:
1.we know the perimeter of the triangle=x-3+x+6+x=3x+3
so,answer is (b)3x+3
2.area of the triangle=1/2*b*h
=1/2*x+2*2x+6=x+2*2x+6/2=2x^2+6x+4x+12/2=2x^2+10x+12/2=2(x^2+5x+6)/2=x^2+5x+6
so,answer is(b)x^2+5x+6
Answer:
In this problem, we are given the following functions:
![f(x)=\frac{1}{2}x](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7B2%7Dx)
and its inverse function:
![f^{-1}(x)=2x](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D2x)
First of all, we want to calculate
. This can be obtained by substituting
x = 2
into f(x). Doing so, we find:
![f(2)=\frac{1}{2}\cdot 2 = 1](https://tex.z-dn.net/?f=f%282%29%3D%5Cfrac%7B1%7D%7B2%7D%5Ccdot%202%20%3D%201)
Then we want to calculate
. We can do it by substituting
x = 1
into
. Doing so,
![f^{-1}(1)=2\cdot 1 = 2](https://tex.z-dn.net/?f=f%5E%7B-1%7D%281%29%3D2%5Ccdot%201%20%3D%202)
Then we want to calculate
, which can be found by calculating f(2) and then using it as input for
We know that
f(2) = 1
Therefore,
![f^{-1}(f(2))=f^{-1}(1)=2](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28f%282%29%29%3Df%5E%7B-1%7D%281%29%3D2)
Then we want to calculate
, which can be calculated by plugging
x = -2
into
. Doing so,
![f^{-1}(-2)=2\cdot (-2)=-4](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28-2%29%3D2%5Ccdot%20%28-2%29%3D-4)
Then we want to calculate
; by substituting
x = 4
into f(x), we find
![f(-4)=\frac{1}{2}\cdot (-4)=-2](https://tex.z-dn.net/?f=f%28-4%29%3D%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%28-4%29%3D-2)
Finally, we want to find ![f(f^{-1}(-2))](https://tex.z-dn.net/?f=f%28f%5E%7B-1%7D%28-2%29%29)
We know already that
![f^{-1}(-2)=-4](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28-2%29%3D-4)
So we have:
![f(f^{-1}(-2))=f(-4)=-2](https://tex.z-dn.net/?f=f%28f%5E%7B-1%7D%28-2%29%29%3Df%28-4%29%3D-2)