Functions 3 Question 3
3. Suppose $f(x)=(x+1)^{2}$ for $x \geq-1$. If $g(x)$ is the function whose graph is reflection of the graph of $f(x)$ with respect to the line $y=x$, then $g(x)$ equals
(2002, 1M)
(a) $-\sqrt{x}-1, x \geq 0$
(b) $\frac{1}{(x+1)^{2}}, x>-1$
(c) $\sqrt{x+1}, x \geq-1$
(d) $\sqrt{x}-1, x \geq 0$
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Answer:
Correct Answer: 3. (a)
Solution:
- According to given information, we have if
$k \in{4,8,12,16,20}$
Then, $f(k) \in{3,6,9,12,15,18}$
$[\because$ Codomain $(f)={1,2,3, \ldots, 20}]$
Now, we need to assign the value of $f(k)$ for
$k \in{4,8,12,16,20}$ this can be done in ${ }^{6} C _5 \cdot 5$ ! ways $=6 \cdot 5 !=6 !$ and remaining 15 element can be associated by 15 ! ways.
$\therefore$ Total number of onto functions $==15 ! 6$ !
