Join IDNLearn.com to access a wealth of knowledge and get your questions answered by experts. Get comprehensive answers to all your questions from our network of experienced experts.

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Find the inverse of the given function.


Sagot :

The inverse of the function, f(x) = (-1/2)√(x + 3), x ≥ -3 is f⁻¹(x) = 4x² - 3, for x ≤ - 1/2.

In the question, we are asked to find the inverse of the function, f(x) = (-1/2)√(x + 3), x ≥ -3.

The domain for the given function is x ≥ -3.

Thus, its range is x ≤ - 1/2.

To find the inverse, we equate f(x) = y, to get:

(-1/2)√(x + 3) = y,

or, √(x + 3) = -2y.

Squaring both sides, we get:

x + 3 = (-2y)²,

or, x + 3 = 4y²,

or, x = 4y² - 3.

Thus, the inverse of the function f(x) = (-1/2)√(x + 3), is, f⁻¹(x) = 4x² - 3.

The inverse will have the domain equal to the range of the original function, that is, x ≤ - 1/2.

Thus, the inverse of the function, f(x) = (-1/2)√(x + 3), x ≥ -3 is f⁻¹(x) = 4x² - 3, for x ≤ - 1/2.

Learn more about the inverse of a function at

https://brainly.com/question/14206391

#SPJ1

The provided question is incomplete. The complete question is:

"Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Find the inverse of the given function.

f(x) = (-1/2)√(x + 3), x ≥ -3

f⁻¹(x) =   x² -   , for x ≤    ."

Your engagement is important to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Thank you for choosing IDNLearn.com for your queries. We’re here to provide accurate answers, so visit us again soon.