Question

The one-to-one function $g$ is defined below. $g(x) = \frac{7x}{2x - 1}$ Find $g^{-1}(x)$, where $g^{-1}$ is the inverse of $g$. Also state the domain and range of $g^{-1}$ in interval notation. $g^{-1}(x) = \Box$ Domain of $g^{-1}$: $\Box$ Range of $g^{-1}$: $\Box$

Name: the one to one function g is defined below gx frac7x2x 1 find g 1x where g 1 is the inverse of g also state the domain and range of g 1 in interval notation g 1x box domain of g 1 box range 15622
Uploaded: 2022-07-06T16:47:27-08:00
Duration: 2 min 38 s
Channel: Gregory Higby
Description: the one to one function g is defined below gx frac7x2x 1 find g 1x where g 1 is the inverse of g also state the domain and range of g 1 in interval notation g 1x box domain of g 1 box range 15622

          The one-to-one function $g$ is defined below.
$g(x) = \frac{7x}{2x - 1}$
Find $g^{-1}(x)$, where $g^{-1}$ is the inverse of $g$.
Also state the domain and range of $g^{-1}$ in interval notation.
$g^{-1}(x) = \Box$
Domain of $g^{-1}$: $\Box$
Range of $g^{-1}$: $\Box$

$the one to one function g is defined below gx frac7x2x 1 find g 1x where g 1 is the inverse of g also state the domain and range of g 1 in interval notation g 1x box domain of g 1 box range 15622$

Added by Thomas F.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Gregory Higby

07/06/2022

Step 1

To find the inverse function $g^{-1}(x)$, we swap $x$ and $y$ and solve for $y$: $x = \frac{7y}{2y - 1}$ $x(2y - 1) = 7y$ $2xy - x = 7y$ $2xy - 7y = x$ $y(2x - 7) = x$ $y = \frac{x}{2x - 7}$ Therefore, $g^{-1}(x) = \frac{x}{2x - 7}$. Show more…

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The one-to-one function $g$ is defined below. $g(x) = \frac{7x}{2x - 1}$ Find $g^{-1}(x)$, where $g^{-1}$ is the inverse of $g$. Also state the domain and range of $g^{-1}$ in interval notation. $g^{-1}(x) = \Box$ Domain of $g^{-1}$: $\Box$ Range of $g^{-1}$: $\Box$