The inverse function is [tex]f^{-1}(x) = \frac{1}{x + 6} + 4[/tex] and the domain is [tex]x \ne 6[/tex]
The function is given as:
[tex]f(x) = \frac{1}{x - 4} - 6[/tex]
Express f(x) as y
[tex]y = \frac{1}{x - 4} - 6[/tex]
Swap the positions of x and y
[tex]x = \frac{1}{y - 4} - 6[/tex]
Add 6 to both sides
[tex]x + 6= \frac{1}{y - 4}[/tex]
Multiply both sides by y-4
[tex](x + 6)(y -4) =1[/tex]
Divide both sides by x + 6
[tex]y - 4 = \frac{1}{x + 6}[/tex]
Add 4 to both sides
[tex]y = \frac{1}{x + 6} + 4[/tex]
Rewrite as:
[tex]f^{-1}(x) = \frac{1}{x + 6} + 4[/tex]
Hence, the inverse function is [tex]f^{-1}(x) = \frac{1}{x + 6} + 4[/tex] and the domain is [tex]x \ne 6[/tex]
Read more about inverse functions at:
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