Question

Find the inverse of the function. y=3 x–3 Write your answer in the form a(bx+c)3+d, where a, b, c, and d are constants. Simplify any fractions. y=

Answer 1

Do you mean a cube root? Your original "y = 3 x–3" is ambiguous. Here are the inverses for the three likely interpretations:

1) If y = 3x − 3 (linear)
- Inverse: y = (x + 3)/3.

2) If y = ∛x − 3 (cube root of x, then minus 3)
- Solve y + 3 = ∛x ⇒ x = (y + 3)^3. Swap variables:
- Inverse: y = (x + 3)^3 (this is in the requested form with a=1, b=1, c=3, d=0).

3) If y = ∛(x − 3) (cube root of (x − 3))
- Solve y = ∛(x − 3) ⇒ y^3 = x − 3 ⇒ x = y^3 + 3. Swap variables:
- Inverse: y = x^3 + 3 (this is in the requested form with a=1, b=1, c=0, d=3).

Which interpretation did you mean?