Step OneFor convenience f(x) = y
y = -(1/2) sqrt(x + 3) Interchange x and y
x = -(1/2) sqrt(y + 3) Multiply both sides by -2
(-2x) = sqrt(y + 3) Square both sides
4x^2 = y + 3 Subtract 3 from both sides
4x^2 -3 = y
f-1(x) = 4x^2 - 3
GraphsThe original graph is in blue
The inverse is red.
Green Line y = x : explained below.
CommentInverses have a very strange property. It acts as a check.
If you perform the following operation
f-1(f(x)) you are left with x
In this case f-1[-1/2 sqrt(x + 3)]= 4(-1/2 * sqrt(x + 3))^2 - 3
f-1 (-1/2sqrt(x+3)) = 4 (1/4 (x+3) - 3
f-1(-1/2sqrt(x + 3)) = x+ 3 - 3 = x
I've included this because I think you have to put the same restriction on f-1(x) as you do on f(x) which is that for f(x) x ≥ -3
This last assertion could be incorrect, but I don't think so.
The answer is f-1(x) = 4x^2 - 3 <<<<<
answer first box and
x≥-3 for the second box. <<<<<<
answer for the second box.Let me know if these are correct. I'm not sure about the restrictions.
Answer:
1.82
Step-by-step explanation:
= 1
= 1.82
Answer:
the present value is 3,162 euros
Step-by-step explanation:
The computation of the present value is shown below:
As we know that
Future value = Present value × (1 + rate of interest)^number of years
3,200 euros = Present value × (1 + 0.012)^1
3,200 euros = Present value × 1.012^1
Present value is
= 3,200 euros ÷ 1.012
= 3,162 euros
Hence, the present value is 3,162 euros
5,125,000 because you divide the amount he has by 0.4 then yo multiply that by 10
Option C (in the figure) is correct.
Step-by-step explanation:
We need to find (f.g)(x)
Given that ![f(x)=2x+1\\g(x)= x^2-7](https://tex.z-dn.net/?f=f%28x%29%3D2x%2B1%5C%5Cg%28x%29%3D%20x%5E2-7)
Now finding (f.g)(x)
![(f.g)(x)= f(x).g(x)](https://tex.z-dn.net/?f=%28f.g%29%28x%29%3D%20f%28x%29.g%28x%29)
![(f.g)(x)= (2x+1)(x^2-7)\\(f.g)(x)=2x(x^2-7)+1(x^2-7)\\(f.g)(x)=2x^3-14x+x^2-7\\(f.g)(x)=2x^3+x^2-14x-7](https://tex.z-dn.net/?f=%28f.g%29%28x%29%3D%20%282x%2B1%29%28x%5E2-7%29%5C%5C%28f.g%29%28x%29%3D2x%28x%5E2-7%29%2B1%28x%5E2-7%29%5C%5C%28f.g%29%28x%29%3D2x%5E3-14x%2Bx%5E2-7%5C%5C%28f.g%29%28x%29%3D2x%5E3%2Bx%5E2-14x-7)
So, ![(f.g)(x)=2x^3+x^2-14x-7](https://tex.z-dn.net/?f=%28f.g%29%28x%29%3D2x%5E3%2Bx%5E2-14x-7)
Option C (in the figure) is correct.
Learn more about Composite Functions at:
brainly.com/question/10772025
brainly.com/question/10541435
Keywords: Composite function
#learnwithBrainly