# Which of the following functions satisfy the condition f(x) = f -1(x)?I) f(x) = -x II) f(x) = √x III) f(x) = -1/x

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We'll calculate the inverse function for the given functions.

We'll note f(x) = y:

y = -x

We'll multiply by -1 and we'll get:

x = -y

f^-1(x) = -x

So f(x) = f^-1(x) for f^-1(x) = -x.

We'll calculate the inverse function for f(x) = sqrtx

y = sqrt x

We'll raise to square both sides:

y^2 = x

f^-1(x) = x^2

We notice that the expression of f(x) is not equal to the expression of f^-1(x) for f(x) = sqrtx.

We'll calculate the inverse function for f(x) = -1/x.

y = -1/x

x*y = -1

x = -1/y

f^-1(x) = -1/x

We notice that f(x) = f^-1(x) for f^-1(x) = -1/x.

We notice that the right answers are I) and III).