Question

The one-to-one function g is defined below. g(x) = \frac{3x-2}{x+8} Find g?¹(x), where g?¹ is the inverse of g. Also state the domain and range of g?¹ in interval notation.

          The one-to-one function g is defined below.
g(x) = \frac{3x-2}{x+8}
Find g?¹(x), where g?¹ is the inverse of g.
Also state the domain and range of g?¹ in interval notation.
        
The one-to-one function g is defined below.
g(x) = (3x-2)/(x+8)
Find g?¹(x), where g?¹ is the inverse of g.
Also state the domain and range of g?¹ in interval notation.

Added by Sheila S.

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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)=(3x-2)/(x+8) 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 8x=3x-2 x+8 Find g1 (), where g1 is the inverse of g. Also state the domain and range of gi in interval notation. 00 0,0[0,0] g=[ 0,0][0,0) Domain of g-1 SE 8 -8 Range of g X 5
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Transcript

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00:01 The 1 to 1 function g is defined below.
00:03 G of x equals 5x minus 4 over 3x plus 8.
00:15 Okay, so find g inverse of x.
00:23 To find g inverse of x, what we do is reset x equals 5y minus 4 over 3y plus 8.
00:43 So i have 3xy plus 8x equals 5y minus 4.
00:55 3xy minus 5y equals negative 4 minus 8x.
01:04 So 5y minus 3xy equals 8x plus 4.
01:11 For the left side, i can factor out y.
01:14 So y times 5 minus 3x equals 4 times x plus 2.
01:21 I divide both sides by 5 minus 3x.
01:24 So i got y equals 4 times x plus 2 divide 5 minus 3x.
01:36 Okay.
01:44 So this is what i got.
01:46 For f inverse, sorry, g inverse of x, 4 times x plus 2 over 5 minus 3x.
02:06 So the domain of g inverse is we set 5 minus 3x.
02:28 Can be 0.
02:31 So 3x is not 5...
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