(x,y) is changed to (x+7,y-7)
It is translated 7 down and 4 to the right.
So , Inverse of
is
.
<u>Step-by-step explanation:</u>
An inverse function is a function that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, and vice versa, i.e., f(x) = y if and only if g(y) = x. As an example, consider the real-valued function of a real variable given by f(x) = 5x − 7. In functional notation this inverse function would be given by,
![{\displaystyle g(y)={\frac {y+7}{5}}}](https://tex.z-dn.net/?f=%7B%5Cdisplaystyle%20g%28y%29%3D%7B%5Cfrac%20%7By%2B7%7D%7B5%7D%7D%7D)
With y = 5x − 7 we have that f(x) = y and g(y) = x. Here we have ![f(x) = \frac{x-7}{x}](https://tex.z-dn.net/?f=f%28x%29%20%20%3D%20%5Cfrac%7Bx-7%7D%7Bx%7D)
![f(x) = \frac{x-7}{x}](https://tex.z-dn.net/?f=f%28x%29%20%20%3D%20%5Cfrac%7Bx-7%7D%7Bx%7D)
⇒ ![f(x) = \frac{x-7}{x}](https://tex.z-dn.net/?f=f%28x%29%20%20%3D%20%5Cfrac%7Bx-7%7D%7Bx%7D)
⇒ ![f(x) =1- \frac{7}{x}](https://tex.z-dn.net/?f=f%28x%29%20%20%3D1-%20%5Cfrac%7B7%7D%7Bx%7D)
Let f(x) = y:
⇒ ![f(x) =1- \frac{7}{x}](https://tex.z-dn.net/?f=f%28x%29%20%20%3D1-%20%5Cfrac%7B7%7D%7Bx%7D)
⇒ ![y = 1 - \frac{7}{x}](https://tex.z-dn.net/?f=y%20%3D%201%20-%20%5Cfrac%7B7%7D%7Bx%7D)
⇒ ![y -1 = \frac{-7}{x}](https://tex.z-dn.net/?f=y%20-1%20%3D%20%5Cfrac%7B-7%7D%7Bx%7D)
⇒ ![x = \frac{-7}{y-1}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-7%7D%7By-1%7D)
So , Inverse of
is
.
<span>This is a tricky question that Reina and Sam are multiplying (84)5 (73)9
and their work are
</span><span>(84)5 (73)9 = 84 + 573 + 9 = 89712 Reina's
(84)5 (73)9 = 84⋅573⋅9 = 820727 Sam's
Actually they are doing or multiplying using exponents.
</span>
Reina’s work
(8⁴)₅(7³)⁹=8⁴⁺⁵+ 7³⁺⁹= 8⁹ 7¹²<span>
This is incorrect because she added exponents
instead of multiplying exponents
Sams work (8</span>⁴<span>)</span>⁵<span> (7</span>³<span>)</span>⁹<span>=8</span>⁴ˣ⁵<span> 7</span>³ˣ⁹<span>= 8</span>²⁰<span> 7</span>²⁷<span>
<span>This is correct because Sam multiplied exponents correctly</span></span>
<span><span>Exponents are multiplied not added.</span></span>
Answer:
Step-by-step explanation:
1. -9x - 21 < -15
2. Add 21 to both sides. -9x < 6
3. Divide both sides by -9.
4. Change the sign.
Final answer:
X > - 6/9