Rewrite the relation as a function of x
4y+cubed root^x=(x-2)^2
4y+∛x = (x-2)^2
4y = (x-2)^2 - ∛x
y = ((x-2)^2 - ∛x)/4
To rewrite the given relation as a function of x, we need to isolate y on one side of the equation.
Starting with the given relation:
4y + ∛x = (x - 2)^2
Step 1: Move the cubic root term to the other side of the equation by subtracting ∛x from both sides:
4y = (x - 2)^2 - ∛x
Step 2: Simplify the right side by cubing the quantity (x - 2):
4y = (x - 2)(x - 2)(x - 2) - ∛x
Step 3: Expand the equation on the right side:
4y = (x^2 - 4x + 4)(x - 2) - ∛x
Step 4: Distribute the terms:
4y = x^3 - 6x^2 + 12x - 8 - ∛x
Step 5: Divide both sides of the equation by 4 to isolate y:
y = (x^3 - 6x^2 + 12x - 8 - ∛x) / 4
Therefore, the rewritten relation as a function of x is:
y = (x^3 - 6x^2 + 12x - 8 - ∛x) / 4
To rewrite the given relation as a function of x, we need to isolate y on one side of the equation.
The given relation is: 4y + ∛x = (x - 2)^2
Step 1: Start by subtracting ∛x from both sides of the equation to move it to the other side:
4y = (x - 2)^2 - ∛x
Step 2: Simplify the right side of the equation using the exponentiation and the cube root:
4y = (x - 2) * (x - 2) * (∛x)^0.33 - ∛x
Step 3: Continue simplifying:
4y = (x - 2) * (x - 2) * x^(0.33/3) - x^(1/3)
Step 4: Expand and simplify further:
4y = (x - 2) * (x - 2) * x^(1/9) - x^(1/3)
Step 5: Multiplying the two terms on the right side:
4y = (x - 2)^2 * x^(1/9) - x^(1/3)
Finally, the rewritten relation as a function of x is:
y = [(x - 2)^2 * x^(1/9) - x^(1/3)] / 4
Now, the relation is expressed as a function of x, where y represents the value of the function for a given x.