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Let f(x)=11-x^(2), x>=0. find and give the domain for f^(-1)(x)

User Smash
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Final answer:

The inverse function of f(x) is f^(-1)(x) = √(11 - x). The domain of f^(-1)(x) is x ≤ 11.

Step-by-step explanation:

The inverse function of f(x) can be found by swapping the x and y variables and solving for y. So, to find f^(-1)(x), we will let y = f^(-1)(x) and solve for x.

Start by replacing f(x) with x in the equation for f(x):

x = 11 - y^2

Next, rearrange the equation to solve for y:

y^2 = 11 - x

Then, take the square root of both sides:

y = ±√(11 - x)

Since x >= 0, we consider only the positive square root:

f^(-1)(x) = √(11 - x)

Therefore, the domain for f^(-1)(x) is all real numbers such that 11 - x ≥ 0, which simplifies to x ≤ 11.

User Ivan Balashov
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