The set of x-intercepts of the function $f ( x ) = 1 + \tan x$ on $[ 0,2 \pi ]$ is

A) $\left\{ \frac { 3 \pi } { 4 } \right\}$
B) $\left\{ \frac { 7 \pi } { 4 } \right\}$
C) $\left\{ \frac { 3 \pi } { 4 } , \frac { 7 \pi } { 4 } \right\}$
D) $\left\{ - \frac { \pi } { 4 } \right\}$
E) $\varnothing$

Question

The set of x-intercepts of the function $f ( x ) = 1 + \tan x$ on $[ 0,2 \pi ]$ is

A) $\left\{ \frac { 3 \pi } { 4 } \right\}$
B) $\left\{ \frac { 7 \pi } { 4 } \right\}$
C) $\left\{ \frac { 3 \pi } { 4 } , \frac { 7 \pi } { 4 } \right\}$
D) $\left\{ - \frac { \pi } { 4 } \right\}$
E) $\varnothing$

Quizplus · Accepted Answer

The x-intercepts occur where $f(x) = 0$, i.e., $1 + \tan x = 0$ or $\tan x = -1$. This happens at $x = \frac{3\pi}{4}$ and $x = \frac{7\pi}{4}$ within the interval $[0, 2\pi]$.

The Set of X-Intercepts of the Function f(x)=1+tan⁡xf ( x ) = 1 + \tan xf(x)=1+tanx

The Set of X-Intercepts of the Function $f ( x ) = 1 + \tan x$