Find the domain of the function f and of its inverse function $\mathrm { f } ^ { - 1 }$ .
-$$f ( x ) = 3 \sin ( 5 x )$$
A) Domain of $f : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ 2,8 ]$

B) Domain of $\mathrm { f } : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ - 5,5 ]$

C) Domain of $\mathrm { f } : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ - 3,3 ]$

D) Domain of $\mathrm { f } : \left[ - \frac { 1 } { 5 } , \frac { 1 } { 5 } \right]$

Domain of $\mathrm { f } ^ { - 1 } : ( - \infty , \infty )$

Question

Find the domain of the function f and of its inverse function $\mathrm { f } ^ { - 1 }$ .
-$$f ( x ) = 3 \sin ( 5 x )$$
A) Domain of $f : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ 2,8 ]$

B) Domain of $\mathrm { f } : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ - 5,5 ]$

C) Domain of $\mathrm { f } : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ - 3,3 ]$

D) Domain of $\mathrm { f } : \left[ - \frac { 1 } { 5 } , \frac { 1 } { 5 } \right]$

Domain of $\mathrm { f } ^ { - 1 } : ( - \infty , \infty )$

Quizplus · Accepted Answer

The domain of $f(x) = 3\sin(5x)$ is all real numbers because the sine function can take any real number as its input, hence $(-\infty, \infty)$. The range of $f(x)$, which becomes the domain of $f^{-1}$, is limited by the amplitude of the sine function, which is 3 in this case, resulting in $[-3, 3]$.

Find the Domain of the Function F and of Its f−1\mathrm { f } ^ { - 1 }f−1

Find the Domain of the Function F and of Its $\mathrm { f } ^ { - 1 }$