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We'll calculate the inverse function for the given functions.
Let 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 get 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 compute 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 the 1st and the 3rd options.
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