The inverse of the function g(x)=-4/3x+2 is
[tex]g^{-1}(x) = -\frac{3}{4}x+\frac{3}{2}[/tex]
The given function is:
[tex]g(x) = -\frac{4}{3}x + 2[/tex]
To find the inverse of the function g(x), follow the steps below
Make x the subject of the formula
[tex]g(x) = -\frac{4}{3}x+2\\\\ -\frac{4}{3}x = g(x) - 2\\\\-4x=3g(x)-6\\\\x = -\frac{3}{4}g(x)+\frac{6}{4} \\\\x = -\frac{3}{4}g(x)+\frac{3}{2}[/tex]
Replace x by [tex]g^{-1}(x)[/tex] and replace g(x) by x
The inverse function therefore becomes:
[tex]g^{-1}(x) = -\frac{3}{4}x+\frac{3}{2}[/tex]
The inverse of the function g(x)=-4/3x+2 is [tex]g^{-1}(x) = -\frac{3}{4}x+\frac{3}{2}[/tex]
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