Find the domain of the function f and of its inverse function f-1.
-$$f ( x ) = - 5 \cos ( 9 x )$$
A) Domain of $f : \left[ - \frac { 1 } { 9 } , \frac { 1 } { 9 } \right]$
Domain of $\mathrm { f } ^ { - 1 } : ( \infty , \infty )$

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

C) Domain of f: $( \infty , \infty )$
Domain of $f ^ { - 1 } : [ - 9,9 ]$

D) Domain of $\mathrm { f } : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ 4,14 ]$

Question

Find the domain of the function f and of its inverse function f-1.
-$$f ( x ) = - 5 \cos ( 9 x )$$
A) Domain of $f : \left[ - \frac { 1 } { 9 } , \frac { 1 } { 9 } \right]$
Domain of $\mathrm { f } ^ { - 1 } : ( \infty , \infty )$

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

C) Domain of f: $( \infty , \infty )$
Domain of $f ^ { - 1 } : [ - 9,9 ]$

D) Domain of $\mathrm { f } : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ 4,14 ]$

Quizplus · Accepted Answer

The cosine function can take any real number as its input, so the domain of $f(x) = -5\cos(9x)$ is all real numbers $(-\infty, \infty)$. The range of the cosine function is $[-1, 1]$, so after multiplying by -5, the range of $f$ becomes $[-5, 5]$, which is the domain of its inverse $f^{-1}$.

Find the Domain of the Function F and of Its f(x)=−5cos⁡(9x)f ( x ) = - 5 \cos ( 9 x )f(x)=−5cos(9x)

Find the Domain of the Function F and of Its $f ( x ) = - 5 \cos ( 9 x )$