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3 years ago

What is the value of x?

Mathematics

1 answer:

Trava [24]3 years ago

7 0

The sum of a polygon's angles are 540.

When you add all the angles together here, you get 456.

Now subtract 456 from 540.

540 - 456 = 84

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Round off 75467 to the nearest thousand

gizmo_the_mogwai [7]

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2 years ago

What is the inverse of this function?

kolbaska11 [484]

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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2 years ago