inverse function and domain and range

**smplease** · May 12th 2008, 08:36 PM

Hey guys the sin is just throwing me out here and I am not to confident with inverse functions

Thanks for any help

Let f (v) = sin v, and g(v) = 1/(2v−1) .
(a) Find g ◦ f and state the domain and range.
(b) Is g(v) one-to-one? Find g−1 (v), the inverse function of g(v), and state the domain and range.

**flyingsquirrel** · May 13th 2008, 11:37 AM

Hi

Originally Posted by smplease

Let f (v) = sin v, and g(v) = 1/(2v−1) .
(a) Find g ◦ f and state the domain and range.

$g\circ f(x)=\frac{1}{2\sin x -1}$ This is a fraction hence it exists iff the denominator does not equal 0 : $2\sin x -1\neq 0 \Longleftrightarrow \sin x \neq \frac{1}{2} \Longleftrightarrow x \neq ?$

To find the range, start from $-1\leq \sin x \leq 1$ then multiply by 2 : $-2\leq 2\sin x \leq 2$ then add 1...

(b) Is g(v) one-to-one? Find g−1 (v), the inverse function of g(v), and state the domain and range.

$g$ is one-to-one iff $g'(x)\neq0$ for any $x$ belonging to the domain of $g$ . To find $g^{-1}$ , you can write $y=\frac{1}{2x-1}$ and solve this for $x$ : it'll give $x=g^{-1}(y)$ .

**smplease** · May 13th 2008, 07:57 PM

Originally Posted by flyingsquirrel

Hi

$g\circ f(x)=\frac{1}{2\sin x -1}$ This is a fraction hence it exists iff the denominator does not equal 0 : $2\sin x -1\neq 0 \Longleftrightarrow \sin x \neq \frac{1}{2} \Longleftrightarrow x \neq ?$

To find the range, start from $-1\leq \sin x \leq 1$ then multiply by 2 : $-2\leq 2\sin x \leq 2$ then add 1...
$g$ is one-to-one iff $g'(x)\neq0$ for any $x$ belonging to the domain of $g$ . To find $g^{-1}$ , you can write $y=\frac{1}{2x-1}$ and solve this for $x$ : it'll give $x=g^{-1}(y)$ .

hey thanks heaps for the help...i'm just still a bit confused with the range. How do I add one to all of that?where do i add it to?

thanks again

**flyingsquirrel** · May 14th 2008, 02:45 AM

Originally Posted by smplease

hey thanks heaps for the help...i'm just still a bit confused with the range. How do I add one to all of that?where do i add it to?

Sorry, I meant

Originally Posted by flyingsquirrel

To find the range, start from $-1\leq \sin x \leq 1$ then multiply by 2 : $-2\leq 2\sin x \leq 2$ then subtract 1...

Thread: inverse function and domain and range

LinkBack

Thread Tools

Display

inverse function and domain and range

Similar Math Help Forum Discussions

Domain/Range of Inverse Trig Function

Find the domain range and inverse

Need help finding the domain and range of this inverse trig function.

Domain/Range, and Inverse

Domain and Range of the Inverse Quadratic Function

Search Tags