Question

Type the correct answer in each box. Use numerals instead of words.

What is the inverse of this function?
f(x=-½√x+3, x≥-3
f^-1(x)=__x²-__, for x ≤__​

Answer 1

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Explanation:

To find the inverse of the given function f(x) = -½√(x + 3), x ≥ -3, we can follow the steps for finding the inverse:

Step 1: Replace f(x) with y.

y = -½√(x + 3)

Step 2: Swap x and y.

x = -½√(y + 3)

Step 3: Solve for y.

Multiply both sides by -2:

-2x = √(y + 3)

Square both sides:

(-2x)^2 = (y + 3)

4x^2 = y + 3

Step 4: Replace y with f^(-1)(x).

f^(-1)(x) = 4x^2 - 3

Therefore, the inverse of the given function is:

f^(-1)(x) = 4x^2 - 3

However, it's worth noting that the domain of the inverse function may be restricted by the domain of the original function. Since the original function has a condition x ≥ -3, the inverse function's domain may be restricted as well.