csat-suneung 2022 Q12

csat-suneung · South-Korea · csat__math 4 marks Curve Sketching Continuity and Discontinuity Analysis of Piecewise Functions

A function $f ( x )$ continuous on the entire set of real numbers satisfies $$\{ f ( x ) \} ^ { 3 } - \{ f ( x ) \} ^ { 2 } - x ^ { 2 } f ( x ) + x ^ { 2 } = 0$$ for all real numbers $x$. When the maximum value of $f ( x )$ is 1 and the minimum value is 0, what is the value of $f \left( - \frac { 4 } { 3 } \right) + f ( 0 ) + f \left( \frac { 1 } { 2 } \right)$? [4 points]
(1) $\frac { 1 } { 2 }$
(2) 1
(3) $\frac { 3 } { 2 }$
(4) 2
(5) $\frac { 5 } { 2 }$

A function $f ( x )$ continuous on the entire set of real numbers satisfies
$$\{ f ( x ) \} ^ { 3 } - \{ f ( x ) \} ^ { 2 } - x ^ { 2 } f ( x ) + x ^ { 2 } = 0$$
for all real numbers $x$. When the maximum value of $f ( x )$ is 1 and the minimum value is 0, what is the value of $f \left( - \frac { 4 } { 3 } \right) + f ( 0 ) + f \left( \frac { 1 } { 2 } \right)$? [4 points]\\
(1) $\frac { 1 } { 2 }$\\
(2) 1\\
(3) $\frac { 3 } { 2 }$\\
(4) 2\\
(5) $\frac { 5 } { 2 }$

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