Answer:
The inverse of f(x) is (x) = ±
+
Step-by-step explanation:
To find the inverse of the quadratic function f(x) = ax² + bx + c, you should put it in the vertex form f(x) = a(x - h)² + k, where
- h =
- k is the vlue f at x = h
∵ f(x) = 3x² - 3x - 2
→ Compare it with the 1st form above to find a and b
∴ a = 3 and b = -3
→ Use the rule of h to find it
∵ h = =
=
∴ h =
→ Substitute x by the value of h in f to find k
∵ k = 3( )² - 3(
) - 2
∴ k =
→ Substitute the values of a, h, and k in the vertex form above
∵ f(x) = 3(x - )² +
∴ f(x) = 3(x - )² -
Now let us find the inverse of f(x)
∵ f(x) = y
∴ y = 3(x - )² -
→ Switch x and y
∵ x = 3(y - )² -
→ Add to both sides
∴ x + = 3(y -
)²
→ Divide both sides by 3
∵ = (y -
)²
→ Take √ for both sides
∴ ± = y -
→ Add to both sides
∴ ± +
= y
→ Replace y by (x)
∴ (x) = ±
+
∴ The inverse of f(x) is (x) = ±
+