Determine what, if any, value to assign to $f ( a )$ to make f continuous at $x = a$ . $f ( x ) = \frac { 3 } { 2 x ^ { 2 } - x }$ ; $a = 0$
A) $f ( 0 ) = - 1$
B) $f ( 0 ) = - 2$
C) $f ( 0 ) = 1$
D) $f ( 0 ) = 0$
E) No value of $f ( 0 )$ will make it continuous at 0.

Question

Determine what, if any, value to assign to $f ( a )$ to make f continuous at $x = a$ .   $f ( x ) = \frac { 3 } { 2 x ^ { 2 } - x }$ ; $a = 0$  
A) $f ( 0 ) = - 1$
B) $f ( 0 ) = - 2$
C) $f ( 0 ) = 1$
D) $f ( 0 ) = 0$
E) No value of $f ( 0 )$ will make it continuous at 0.

Quizplus · Accepted Answer

For a function to be continuous at $x = a$, the limit as $x$ approaches $a$ must exist and be equal to the function's value at $a$. In this case, as $x$ approaches 0, the denominator of $f(x) = \frac{3}{2x^2 - x}$ approaches 0, causing the function to approach infinity or negative infinity, depending on the direction from which $x$ approaches 0. Therefore, no finite value assigned to $f(0)$ can make $f(x)$ continuous at $x = 0$.

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