Consider f(x)=x(x2+6 x+8)(x2-6 x+5), g(x)=x2-3 x-10 and h(x)=(f(x)/g(x)), then number of integers not in the range of h(x) are

Question

Consider f(x)=x(x2+6 x+8)(x2-6 x+5), g(x)=x2-3 x-10 and h(x)=(f(x)/g(x)), then number of integers not in the range of h(x) are (A) 0 (B) 1 (C) 2 (D) 3

Tardigrade Admin · Accepted Answer

h(x)=(x(x+2)(x+4)(x-5)(x-1)/(x-5)(x+2)) h(x)=x(x+4)(x-1), x ≠ 5,-2 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/e49c9451dff3cf4a596bd1265356233b-.png" /> Clearly h(-2) is contained in range of h but h(5) is not contained in range of h.

Q. Consider $f (x) = x (x^{2} + 6 x + 8) (x^{2} - 6 x + 5), g (x) = x^{2} - 3 x - 10$ and $h (x) = \frac{f ( x )}{g ( x )}$ , then number of integers not in the range of $h (x)$ are

0

1

2

3

$h (x) = \frac{x ( x + 2 ) ( x + 4 ) ( x - 5 ) ( x - 1 )}{( x - 5 ) ( x + 2 )}$
$h (x) = x (x + 4) (x - 1), x \neq = 5, - 2$

Clearly $h (- 2)$ is contained in range of $h$ but $h (5)$ is not contained in range of $h$ .

Q. Consider f(x)=x(x2+6x+8)(x2−6x+5),g(x)=x2−3x−10 and h(x)=g(x)f(x)​, then number of integers not in the range of h(x) are

0

1

2

3

h(x)=(x−5)(x+2)x(x+2)(x+4)(x−5)(x−1)​ h(x)=x(x+4)(x−1),x=5,−2 Clearly h(−2) is contained in range of h but h(5) is not contained in range of h.

Q. Consider $f (x) = x (x^{2} + 6 x + 8) (x^{2} - 6 x + 5), g (x) = x^{2} - 3 x - 10$ and $h (x) = \frac{f ( x )}{g ( x )}$ , then number of integers not in the range of $h (x)$ are

$h (x) = \frac{x ( x + 2 ) ( x + 4 ) ( x - 5 ) ( x - 1 )}{( x - 5 ) ( x + 2 )}$
$h (x) = x (x + 4) (x - 1), x \neq = 5, - 2$

Clearly $h (- 2)$ is contained in range of $h$ but $h (5)$ is not contained in range of $h$ .