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romanna [79]
2 years ago
11

What is the inverse of this function?​

Mathematics
1 answer:
kolbaska11 [484]2 years ago
5 0

Answer:

f^{-1}(x)=4x^2-3

Step-by-step explanation:

<u>The Inverse of a Function</u>

Given a function f(x), the inverse of f, called f^{-1}(x) is a function that satisfies:

f(f^{-1}(x))=x

The domain of f becomes the range of its inverse and vice-versa.

The procedure to find the inverse of the function is:

* Write the function as a two-variable equation:

* Solve the equation for x.

* Swap the variables

We are given the function:

\displaystyle f(x)=-\frac{1}{2}\sqrt{x+3}

Defined in the interval x ≥ -3

Note f is always negative, thus its range is f(x) ≤ 0

Now we find the inverse. Call y=f(x):

\displaystyle y=-\frac{1}{2}\sqrt{x+3}

Multiplying by 2:

\displaystyle 2y=-\sqrt{x+3}

Squaring both sides:

\displaystyle 4y^2=x+3

Subtracting 3:

\displaystyle 4y^2-3=x

Swapping variables:

y=4x^2-3

Thus:

\mathbf{f^{-1}(x)=4x^2-3}

The domain of the inverse is the range of f, thus x is restricted to

x ≤ 0

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4 0
2 years ago
the theaters sell tickets for a concert. tickets for the lower level are $35 each and tickets for the upper level are $25 each.
nasty-shy [4]
Equation 1 for tickets sold:
$35x + $25y = $10,250

Equation 2 for quantity (number #) of tickets sold:
x + y = 350

Use substitution method:

y = 350 - x

35x + 25 (350 - x) = $10,250

35x + $8750 - 25x = $10,250

10x + $8750 = $10,250
- $8,750 -$8,750

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Check the answers:

$35 (150) + $25 (200) =

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4 0
2 years ago
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poizon [28]
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3 years ago
A car dealer sells four model types: A,B,C,D. On a given week, this dealer sold 10 cars of model A, 5 of model B, 8 of model C a
olasank [31]

Answer:

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Step-by-step explanation:

i hope its help

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Answer:

-5/2

Step-by-step explanation:

2x + 9 = 4

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