IDNLearn.com provides a platform for sharing and gaining valuable knowledge. Join our interactive community and access reliable, detailed answers from experienced professionals across a variety of topics.
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 ≤ ."