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

B) Domain of $f : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ - 8 , - 2 ]$

C) Domain of $\mathrm { f } : ( \infty , \infty )$
Domain of $f ^ { - 1 } : [ 2,8 ]$

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

Question

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

B) Domain of $f : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ - 8 , - 2 ]$

C) Domain of $\mathrm { f } : ( \infty , \infty )$
Domain of $f ^ { - 1 } : [ 2,8 ]$

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

Quizplus · Accepted Answer

The function $f(x) = 3\sin x - 5$ is defined for all real numbers because the sine function has a domain of all real numbers, hence $f$ has a domain of $(-\infty, \infty)$. The range of $f(x)$ is $[-8, -2]$ because the sine function varies between -1 and 1, and after scaling and shifting, the output values are between -8 and -2. The domain of the inverse function $f^{-1}$ is the range of the original function, hence $[-8, -2]$.

Find the Domain of the Function F and of Its f(x)=3sin⁡x−5f ( x ) = 3 \sin x - 5f(x)=3sinx−5

Find the Domain of the Function F and of Its $f ( x ) = 3 \sin x - 5$