The function f(x) is given by The inverse of f(x)
The function f(x) is given by (2x-1) ² . The inverse of f(x) is given by
- A.
√(x) + 1/2
- B.
(2√(x) + 1) / 2
- C.
1/2(√(x))
- D.
1/2(√(x) + 1)
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Correct answer: D
Step 1: Write the Function
y=(2x−1)2
Step 2: Solve for x
Take the square root of both sides:
√y=2x−1
(Note: We consider the positive square root because f(x) is defined for y≥0.)
Solve for x:
2x=√y+1
x =
Step 3: Write the Inverse Function
Replace y with x to express the inverse function:
f−1(x) =
