Assertion (A): The function f(x)=x^2+b x+c where b and c are real… - Vidyadip

Question

Assertion (A): The function $f(x)=x^2+b x+c$ where b and c are real constants, describes onto mapping.
Reason (R): Let $A=\{1, 2, 3, \ldots, n \}$ and $B =\{ a , b \}$. Then, the number of surjections from A into B is $2^{ n }-2$.

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Answer

(d) A is false but R is true.
Explanation:
Assertion: Given function is $f(x)=x^2+b x+c$
It is a quadratic equation in x.
So, we will get a parabola either downward or upward.
Hence, it is a many-one mapping and not onto mapping.
Hence, it is neither one-one nor onto mapping.
Reason: Total number of functions $=( n ( B ))^{ n ( A )}=2^{ n }$
Clearly, a function will not be onto if all elements of A map to either a or b

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