Question

4) Let $f(x) = \frac{1}{\sqrt{16+6x-x^2}}$. Find the correct answer A) $f(x)$ is continuous at all points on $[-2, 8]$. B) $f(x)$ is continuous at all points on $(-2, 8)$. C) $f(x)$ is continuous at all points except $x = -2$ and $x = 8$. D) $f(x)$ is continuous at all points except $x = -2$. E) $f(x)$ is continuous at all points on $(-\infty, -2) \cup (8, \infty)$.

Name: 4 let fx frac1sqrt166x x2 find the correct answer a fx is continuous at all points on 2 8 b fx is continuous at all points on 2 8 c fx is continuous at all points except x 2 and x 8 d fx is 91027
Uploaded: 2024-02-08T08:59:33-08:00
Duration: 3 min
Channel: Shu Naito
Description: 4 let fx frac1sqrt166x x2 find the correct answer a fx is continuous at all points on 2 8 b fx is continuous at all points on 2 8 c fx is continuous at all points except x 2 and x 8 d fx is 91027

          4) Let $f(x) = \frac{1}{\sqrt{16+6x-x^2}}$.
Find the correct answer
A) $f(x)$ is continuous at all points on $[-2, 8]$.
B) $f(x)$ is continuous at all points on $(-2, 8)$.
C) $f(x)$ is continuous at all points except $x = -2$ and $x = 8$.
D) $f(x)$ is continuous at all points except $x = -2$.
E) $f(x)$ is continuous at all points on $(-\infty, -2) \cup (8, \infty)$.

$4 let fx frac1sqrt166x x2 find the correct answer a fx is continuous at all points on 2 8 b fx is continuous at all points on 2 8 c fx is continuous at all points except x 2 and x 8 d fx is 91027$

Added by Alex J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shu Naito

02/08/2024

Step 1

The expression inside the square root is $16+6x-x^2$. We need to find when this is positive: $16+6x-x^2 > 0$ $x^2 - 6x - 16 < 0$ $(x-8)(x+2) < 0$ This inequality holds when $-2 < x < 8$. Therefore, $f(x)$ is continuous on the interval $(-2, 8)$. Show more…

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4) Let $f(x) = \frac{1}{\sqrt{16+6x-x^2}}$. Find the correct answer A) $f(x)$ is continuous at all points on $[-2, 8]$. B) $f(x)$ is continuous at all points on $(-2, 8)$. C) $f(x)$ is continuous at all points except $x = -2$ and $x = 8$. D) $f(x)$ is continuous at all points except $x = -2$. E) $f(x)$ is continuous at all points on $(-\infty, -2) \cup (8, \infty)$.