Find the domain of the function f and of its inverse function f-1.
-$$f ( x ) = 6 \tan x + 10$$
A) Domain of $f : ( \infty , \infty )$
$\mathrm { f } ^ { - 1 } : [ 4,16 ]$

B) Domain of $f : x \neq \frac { ( 2 k + 1 ) \pi } { 2 } ; k$ an integer Domain of
Domain of $f ^ { - 1 } : ( \infty , \infty )$

C) Domain of $\mathrm { f } : ( \infty , \infty )$
Domain of $f ^ { - 1 } : x \neq \frac { ( 2 k + 1 ) \pi } { 2 } ; k$ an integer

D) Domain of $f : x \neq \frac { ( 2 k + 1 ) \pi } { 2 } ; k$ an integer
Domain of $\mathrm { f } ^ { - 1 } : [ 4,16 ]$

Question

Find the domain of the function f and of its inverse function f-1.
-$$f ( x ) = 6 \tan x + 10$$
A) Domain of $f : ( \infty , \infty )$
$\mathrm { f } ^ { - 1 } : [ 4,16 ]$

B) Domain of $f : x \neq \frac { ( 2 k + 1 ) \pi } { 2 } ; k$ an integer Domain of 
Domain of $f ^ { - 1 } : ( \infty , \infty )$

C) Domain of $\mathrm { f } : ( \infty , \infty )$
Domain of $f ^ { - 1 } : x \neq \frac { ( 2 k + 1 ) \pi } { 2 } ; k$ an integer

D) Domain of $f : x \neq \frac { ( 2 k + 1 ) \pi } { 2 } ; k$ an integer
Domain of $\mathrm { f } ^ { - 1 } : [ 4,16 ]$

Quizplus · Accepted Answer

The function $f(x) = 6\tan(x) + 10$ is defined for all $x$ except where $\tan(x)$ is undefined, which occurs at $x = \frac{(2k+1)\pi}{2}$, where $k$ is an integer. The inverse function $f^{-1}$ swaps the domain and range of $f$, and since the range of $f$ is all real numbers (because $\tan(x)$ can take any real value), the domain of $f^{-1}$ is also all real numbers $(-\infty, \infty)$.

Find the Domain of the Function F and of Its f(x)=6tan⁡x+10f ( x ) = 6 \tan x + 10f(x)=6tanx+10

Find the Domain of the Function F and of Its $f ( x ) = 6 \tan x + 10$