If y=f(x)=(x+2)/(x-1), then it is incorrect to say:

1952 AMC 12 Problem 11

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11.

y=f(x)=\dfrac{x+2}{x-1},

then it is incorrect to say:

x=\dfrac{y+2}{y-1}

f(0)=-2

f(1)=0

f(-2)=0

f(y)=x

Check the domain of the rational function before evaluating it

The denominator vanishes at one of the listed inputs

The function is undefined at

x=1

because its denominator is zero there, so

f(1)=0

is false. The other statements hold:

f(0)=-2,

f(-2)=0,

solving

y=\frac{x+2}{x-1}

gives

x=\frac{y+2}{y-1},

and this same formula shows that

f

is its own inverse.

Thus, the correct answer is C.