Please help as soon as possible

Mathematics

1 answer:

ch4aika [34]3 years ago

8 0

To solve this problem you must apply the proccedure shown below:

You must switch the variables, and then, you must solve for $y$ , as following:

$x=-\frac{1}{2} \sqrt{y} +3\\ (x-3)^{2} = (\frac{1}{2}\sqrt{y})^{2} \\ y=4x^{2} -24x+36\\ f^{-1} (x)=4x^{2} -24x+36$

Therefore, as you can see, the answer is: $f^{-1} (x)= 4x^{2} -24x+36
$

You might be interested in

Check my Work: Factoring for 2y^+9y-18 is (2y-3) (y+6) true or false?

Alexxandr [17]

It is true because when you separate 2y^2 +9y -18, you are supposed to get the factors (2y-3)(y+6), when you multiply this it gives you the first equation, we know this because when we multiply the first term it gives us exactly 2y^2 and if we multiply the last ones it gives you -18, now here is the tricky part, when we multiply the middle part we get 12y and -3y, when we add these up we get 9y, now is that the same middle as in the equation? Yes… then our factors are correct making this true

Hope this helps

7 0

2 years ago

A new hospital tracked the number of births during its first 6 months of operation, as shown in the table. Find a quadratic func

UNO [17]

Let x refers to the Month numbers
And y refers to Number of births

There is 5 steps to find the quadratic function that models the data.

First step ⇒ Plot the data pairs (x, y) in a coordinate plane.
 which are the blue circles in the attached figure

Second step ⇒ Draw the parabola you think best fits the data.
 Which is the red function in the attached figure.

Third step ⇒ Estimate the coordinates of three points on the
 parabola, which are (2, 108), (4, 68), and (6, 75).
 which are the black squares in the attached figure

Fourth step ⇒ Substitute the coordinates of the points into the model 
 y = ax2 + bx + c
 to obtain a system of three linear equations.

 4a + 2 b + c = 108 ---------(1)
 16a + 4 b + c = 68 ---------(2)
36a + 6 b + c = 75 ---------(3)

Fifth step ⇒ Solve the linear system.
 By using the calculator
 a = 5.875 , b = -55.25 , c = 195

So, the quadratic model for the data is ⇒ y = 5.875 x²- 55.25 x + 195
============================================
To predict the number of births for month 8
substitute with x = 8 ⇒ y = 5.875 * 8²- 55.25 * 8 + 195 = 129