Question

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

Answer 1

Given function :-

$\bf \implies g(x) = \dfrac{3}{x}+7$

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

$\bf \implies y = \dfrac{3}{x}+7$

• Interchange x and y .

$\bf \implies x = \dfrac{3}{y}+7$

• Solve for y .

$\bf\implies \dfrac{3}{y}= x -7 \\\\\bf\implies y =\dfrac{3}{x-7}$

• Replace y with f-¹(x) .

$\implies\boxed{\red{\bf f^{-1}(x) = \dfrac{3}{x-7} }}$