SATHEE: Functions 3 Question 3

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) $\frac{1}{(x + 1)^{2}}, x > - 1$

(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, $f (k) \in 3, 6, 9, 12, 15, 18$

$[∵$ Codomain $(f) = 1, 2, 3, \dots, 20]$

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.

$∴$ Total number of onto functions $== 15! 6$ !

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Functions 3 Question 3

3. Suppose f(x)=(x+1)2 for x≥−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

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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