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:

$y=-\frac{1}{2}\sqrt{x+1} \\ x=\frac{1}{2}\sqrt{y+1}\\ x^{2} =(\frac{1}{2}\sqrt{y+1})^{2}\\ x^{2} =\frac{1}{4}(y+1)\\ y=4x^{2} -1$

2. Therefore, you have:

$f^{-1}(x)=4x^{2} -1$

The answer is: $f^{-1}(x)=4x^{2} -1$

Answer 2

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