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what is the inverse of g?
g(x) = 3/x+7

Sagot :

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Given function :-

[tex]\bf \implies g(x) = \dfrac{3}{x}+7[/tex]

  • To find its reverse , substitute y = g(x) .

[tex]\bf \implies y = \dfrac{3}{x}+7[/tex]

  • Interchange x and y .

[tex]\bf \implies x = \dfrac{3}{y}+7[/tex]

  • Solve for y .

[tex]\bf\implies \dfrac{3}{y}= x -7 \\\\\bf\implies y =\dfrac{3}{x-7} [/tex]

  • Replace y with f-¹(x) .

[tex]\implies\boxed{\red{\bf f^{-1}(x) = \dfrac{3}{x-7} }}[/tex]

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