What is the inverse of f(x)=(x-2)^3

g⁻¹(x) = 2 + ∛x

Step-by-step explanation:

g(x) = (x - 2)³     Rename g(x) as y

   y = (x - 2)³

Solve for x :

        y = (x - 2)³     Multiply each side by 3

     ∛y =  x - 2         Add 2 to each side

∛y + 2 = x  

        x = ∛y + 2      Switch x and y

        y = ∛x + 2      Rename y as g inverse

 g⁻¹(x) = 2 + ∛x

See the graphs of g(x) and g⁻¹(x) below.

g(x) is the red line. g⁻¹(x) is the blue line.

Each graph reflects the other about the dashed line representing the function y = x.

to determine the unit cost your would divide the total cost by the number sold.

7 bagels for $4.41       $4.41/7 = $.63 each at fresh side

5 bagels for $3.60         $3.60/5 = $.72 each at value mart

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240