Given:
The function is
![m(x)=x^2-17x](https://tex.z-dn.net/?f=m%28x%29%3Dx%5E2-17x)
To find:
The inverse of the given function.
Solution:
We have,
![m(x)=x^2-17x](https://tex.z-dn.net/?f=m%28x%29%3Dx%5E2-17x)
Substitute m(x)=y.
![y=x^2-17x](https://tex.z-dn.net/?f=y%3Dx%5E2-17x)
Interchange x and y.
![x=y^2-17y](https://tex.z-dn.net/?f=x%3Dy%5E2-17y)
Add square of half of coefficient of y , i.e.,
on both sides,
![x+\left(\dfrac{-17}{2}\right)^2=y^2-17y+\left(\dfrac{-17}{2}\right)^2](https://tex.z-dn.net/?f=x%2B%5Cleft%28%5Cdfrac%7B-17%7D%7B2%7D%5Cright%29%5E2%3Dy%5E2-17y%2B%5Cleft%28%5Cdfrac%7B-17%7D%7B2%7D%5Cright%29%5E2)
![x+\left(\dfrac{17}{2}\right)^2=y^2-17y+\left(\dfrac{17}{2}\right)^2](https://tex.z-dn.net/?f=x%2B%5Cleft%28%5Cdfrac%7B17%7D%7B2%7D%5Cright%29%5E2%3Dy%5E2-17y%2B%5Cleft%28%5Cdfrac%7B17%7D%7B2%7D%5Cright%29%5E2)
![[\because (a-b)^2=a^2-2ab+b^2]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%28a-b%29%5E2%3Da%5E2-2ab%2Bb%5E2%5D)
Taking square root on both sides.
![\sqrt{x+\left(\dfrac{17}{2}\right)^2}=y-\dfrac{17}{2}](https://tex.z-dn.net/?f=%5Csqrt%7Bx%2B%5Cleft%28%5Cdfrac%7B17%7D%7B2%7D%5Cright%29%5E2%7D%3Dy-%5Cdfrac%7B17%7D%7B2%7D)
Add
on both sides.
![\sqrt{x+\left(\dfrac{17}{2}\right)^2}+\dfrac{17}{2}=y](https://tex.z-dn.net/?f=%5Csqrt%7Bx%2B%5Cleft%28%5Cdfrac%7B17%7D%7B2%7D%5Cright%29%5E2%7D%2B%5Cdfrac%7B17%7D%7B2%7D%3Dy)
Substitute
.
![m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}](https://tex.z-dn.net/?f=m%5E%7B-1%7D%28x%29%3D%5Csqrt%7Bx%2B%28%5Cdfrac%7B189%7D%7B4%7D%7D%29%2B%5Cdfrac%7B17%7D%7B2%7D)
We know that, negative term inside the root is not real number. So,
![x+\left(\dfrac{17}{2}\right)^2\geq 0](https://tex.z-dn.net/?f=x%2B%5Cleft%28%5Cdfrac%7B17%7D%7B2%7D%5Cright%29%5E2%5Cgeq%200)
![x\geq -\left(\dfrac{17}{2}\right)^2](https://tex.z-dn.net/?f=x%5Cgeq%20-%5Cleft%28%5Cdfrac%7B17%7D%7B2%7D%5Cright%29%5E2)
Therefore, the restricted domain is
and the inverse function is
.
Hence, option D is correct.
Note: In all the options square of
is missing in restricted domain.
Answer:
40x + 1500>3500 is the correct answer.
Step-by-step explanation:
Answer:
ita A hope it helps
Step-by-step explanation:
Answer:
Slope of function B
Step-by-step explanation:
One pound is equivalent to 16 ounces.
Thus, multiply 14 pounds with 16 to get the number of ounces.
![14 \times 16 = 224](https://tex.z-dn.net/?f=14%20%5Ctimes%2016%20%3D%20224)
14 pounds equals 224 ounces. Let me know if you need any clarifications, thanks!
~ Padoru