The actual inverse function is:
![f^{-1}(x) = x^2 + 3](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%20%3D%20x%5E2%20%2B%203)
And the domain is [0, ∞).
<h3>
Where is the mistake?</h3>
Remember that for a given function f(x) with a domain D and a range R.
For the inverse function, f⁻¹(x) the domain is R and the range is D.
Here, for the given function the domain is x ≥ 3 and the range is [0, ∞).
Then for the inverse function, which is:
![f^{-1}(x) = x^2 + 3](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%20%3D%20x%5E2%20%2B%203)
(to check this, you must have that):
![f^{-1}(f(x)) = x\\\\f(f^{-1}(x)) = x](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28f%28x%29%29%20%3D%20x%5C%5C%5C%5Cf%28f%5E%7B-1%7D%28x%29%29%20%3D%20x)
The domain will be [0, ∞) and the range x ≥ 3
If you want to learn more about inverse functions:
brainly.com/question/14391067
#SPJ1
Answer:
Greatest number: 9
Least number: 2
Range: 7
Step-by-step explanation:
From smallest to largest, the numbers are: 2, 3, 6, 8, 9. The largest (greatest) is 9 and the least (smallest) is 2. The range is 9-2=7.
Answer:
- 6x³ - 1
Step-by-step explanation:
Substitute x = g(x) into f(x), that is
(f ○ g)(x)
= f(x³ )
= - 6(x³) - 1
= - 6x³ - 1
180
Explanation:
Set a equation of a ratio 120/90=x/135
And calculate!
90x=(120)(135)
90x=16200
x=180