PLEASE HELP

2 answers:

7 0

Our function. y=(x^2 ) +6
The inverse function switches from (x,y) to (y, x) so where you see y put a x and where you see x put a y.
Inverse function. X=(y^2)+6
Now we still needed to have it in the form of y= something so lets work it.
X-6=y^2
Square root (x-6)=y
f^-1 (x)=square root (x-6)

klio [65]3 years ago

3 0

f(x)=x^2−6

Replace f(x) with yy.

y=x^2−6

Interchange the variables.

x=y2−6

Solve for yy.

Move −6-6 to the right side of the equation by subtracting −6-6 from both sides of the equation.y2=6+xy2=6+xTake the squaresquare root of both sides of the equationequation to eliminate the exponent on the left side.y=±√6+xy=±6+x

The complete solution is the result of both the positive and negative portions of the solution.

Tap for more steps...

y=√6+x,−√6+x
Solve for y and replace with f^−1(x).

Answer is f−1(x)=√6+x,−√6+x

You might be interested in

20. what us the area of the figure:

Varvara68 [4.7K]

If the angle in B is 45º, that means the angle in A is also going to be 45º, considering it's a right triangle, so AC and BC are they have the same length.
Then using Pythagoras, you'll get that $AC^{2} + BC^{2}$ equals $AB^{2}$ .
Now, you know that AC=BC and that AB=24.
So you'll get $2AC^{2} =24^2$ . You do the square root in both sides and you get that 2AC=24 and AC=12.

Now that you know that both AC and BC equal 12, you can find the area by just multiplying them and then diving them by 2. (The formula for the area of a triangle is half base multiplied by height, and in a right triangle, if a cathetus is the base, the other cathetus will be the height)

And so the area is equal to 72.

8 0

3 years ago

A model rocket is launched with an intitial upupward velocity of 202 ft/s. The rocket’s height h (in feet) after seconds is give

dsp73

Given that the height of a object thrown within a gravitational field is given as a quadratic equation in time, t, the time at which the object is at a specified height can be found by the quadratic formula

The values of, t, for which the height of the rocket is 82 feet are;

t = 12.21 seconds or t = 0.42 seconds

Question: Parts of the question that appear missing but can be found online are (i) To find the values of the time, t, when the rocket's height is 82 feet and round answers to the nearest hundredth

The known parameters of the rocket are;

The initial upward velocity of the rocket, v = 202 ft./s

The given function representing the height, h, (in feet) after t seconds is presented as follows;

H = 202·t - 16·t²

The unknown;

The time for which the height of the rocket is 82 feet

Method;

Substitute H = 82 feet in the height function equation and solve for t as follows;

When H = 82, we get;

82 = 202·t - 16·t²

Therefore;

16·t² - 202·t + 82 = 0