Question

The one-to-one function $g$ is defined below. $g(x) = \frac{7x}{7-6x}$ 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) = \[\] Domain of $g^{-1}$ : \[\] Range of $g^{-1}$ : \[\]

          The one-to-one function $g$ is defined below.
$g(x) = \frac{7x}{7-6x}$
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) = \[\]
Domain of $g^{-1}$ : \[\]
Range of $g^{-1}$ : \[\]
        
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The one-to-one function g is defined below.
g(x) = (7x)/(7-6x)
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) = 
    

Domain ofg^-1: 
    

Range ofg^-1:

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Elementary and Intermediate Algebra
Elementary and Intermediate Algebra
Alan S. Tussy, R. David Gustafson 5th Edition
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The one-to-one function g is defined below. g(x) = 7x Find g(x), where g is the inverse of g. Also state the domain and range of g in interval notation. g(x) = 1 Domain of g: (-∞, ∞) Range of g: (-∞, ∞)
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Transcript

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00:01 Hi there.
00:02 Let's start off solving this question by finding the domain of the function g of x.
00:08 So this is a fraction, so the denominator cannot be zero.
00:12 That means if 5x plus 9 is equal to 0, we got x is equal to negative 9 over 5.
00:18 That means x cannot be this value.
00:20 So the domain of the function for g of x, which is all real numbers except negative 9 over 5, and that goes to the range.
00:32 So for the range of the function, we have to find the inverse of this function.
00:37 So for the inverse of the function, let's say g of x is equal to y.
00:41 So g of x is equal to y.
00:43 That is equal to 9x minus 1 over 5x minus 9.
00:48 So the inverse of the function, what we have to do, this is 5x plus 9 here.
00:54 So if i just do the cross multiplication, we need to just leave x alone.
00:58 So first of all, do cross multiplication, which is 5xy plus 9y, which is equal to 9x minus 1.
01:06 Let's move x values to the one side and the y values to the other side...
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