Let f(x)=(1/x), g(x)=(1/4 x2-1) and h(x)=(5 x/x+2) be three functions and k(x)=h(g(f(x))). If domain and range of k(x) are R- a1, a2, a3, ldots . an and R-A respectively where 'R' is the set of real numbers then

Question

Let f(x)=(1/x), g(x)=(1/4 x2-1) and h(x)=(5 x/x+2) be three functions and k(x)=h(g(f(x))). If domain and range of k(x) are R- a1, a2, a3, ldots . an and R-A respectively where 'R' is the set of real numbers then (A)  n + displaystyle∑ i =1 n a i =5 (B) n + displaystyle∑ i =1 n a i =10 (C) number of integers in set A is 5 (D) Number of integers in set A is 7.

Tardigrade Admin · Accepted Answer

k ( x )= h ( g ( f ( x )))=(5 x 2/8- x 2) text Domain of k ( x ) text is R - 0, ± 2, ± 2 √2 text Range of k ( x ) text is (-∞,-5) ∪(0, ∞)- 5 text or R -([-5,0] ∪ 5 ) ∴ A text is [5,0] ∪ 5

Q. Let $f (x) = \frac{1}{x}, g (x) = \frac{1}{4 x ^{2} - 1}$ and $h (x) = \frac{5 x}{x + 2}$ be three functions and $k (x) = h (g (f (x)))$ . If domain and range of $k (x)$ are $R - {a_{1}, a_{2}, a_{3}, \dots . a_{n}}$ and $R - A$ respectively where 'R' is the set of real numbers then

$n + i = 1 \sum n a_{i} = 5$

$n + i = 1 \sum n a_{i} = 10$

number of integers in set A is 5

Number of integers in set $A$ is 7.

$k (x) = h (g (f (x))) = \frac{5 x ^{2}}{8 - x ^{2}}$
$Domain of k (x) is R - {0, \pm 2, \pm 22}$
$Range of k (x) is (- \infty, - 5) \cup (0, \infty) - {5}$
$or R - ([- 5, 0] \cup {5})$
$∴ A is [5, 0] \cup {5}$

Q. Let f(x)=x1​,g(x)=4x2−11​ and h(x)=x+25x​ be three functions and k(x)=h(g(f(x))). If domain and range of k(x) are R−{a1​,a2​,a3​,….an​} and R−A respectively where 'R' is the set of real numbers then

n+i=1∑n​ai​=5

n+i=1∑n​ai​=10