Find the inverse of the given function. f(x)= -1/2*square root of (x+1), x greater than equal to -3

1. First, you must change for . Then, you need to switch and and solve for , as following:

2. Therefore, you have:

The answer is:

Answer

f⁻¹(x) = 4x² - 1

f⁻¹(x) ≥ 35

Explanation

The function to find the inverse for is;

f(x) = -1/2 × √(x-1), x ≥ -3

First equat the function to y the make x the subject of the formula.

y = -1/2 × √(x-1)

Square both sides of the equation

y² = 1/4 ×(x+1)

Multiplying both sides by 4

4y² = x+1

Subtracting 1 from both sides.

x = 4y² - 1

Now interchange x and y.

y = 4x² - 1

The inverse of f(x) = 1/2 × √(x-1) is;

f⁻¹(x) = 4x² - 1 , x ≥ -3

f⁻¹(x) = 4×(-3)² -1

= (4×9) - 1

=36 - 1

=35

Answer,

f⁻¹(x) ≥ 35

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2