Question

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

Answer 1

1. First, you must change
`f(x)` for
`y`. Then, you need to switch
`x` and
`y` and solve for
`y`, as following:

`y=-(1)/(2)√(x+1) \\ x=(1)/(2)√(y+1)\\ x^(2) =((1)/(2)√(y+1))^(2)\\ x^(2) =(1)/(4)(y+1)\\ y=4x^(2) -1`

2. Therefore, you have:

`f^(-1)(x)=4x^(2) -1`

The answer is:
`f^(-1)(x)=4x^(2) -1`

Answer 2

f⁻¹(x) = 4x² - 1

f⁻¹(x) ≥ 35

Step-by-step 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