ARE THE FOLLOWING EQUATIONS INVERSES?
y=x^4-7 and y=∜ x+7
To determine if the given equations are inverses of each other, we need to follow a specific process.
Step 1: Write down the first equation: y = x^4 - 7.
Step 2: Replace y with x and x with y in the equation: x = y^4 - 7.
Step 3: Solve the equation for y in terms of x: y^4 = x + 7.
Step 4: Take the fourth root of both sides to solve for y: ∜y^4 = ∜(x + 7).
Step 5: Simplify: y = ∜(x + 7).
Now, let's compare this equation with the second given equation: y = ∜(x + 7).
Since both equations are the same, y = ∜(x + 7), we can conclude that the given equations are inverses of each other.