Questions: Find the inverse of the following function: g(x) = 6/x + 2

Transcript text: Find the inverse of the following function: \[ g(x)=\frac{6}{x}+2 \]

Solution

Solution Steps

Step 1: Replace $g(x)$ with $y$

We have the function $g(x) = \frac{6}{x} + 2$. We replace $g(x)$ with $y$: \[ y = \frac{6}{x} + 2 \]

Step 2: Swap $x$ and $y$

Swap $x$ and $y$ in the equation: \[ x = \frac{6}{y} + 2 \]

Step 3: Solve for $y$

Subtract 2 from both sides: \[ x - 2 = \frac{6}{y} \] Multiply both sides by $y$: \[ y(x-2) = 6 \] Divide both sides by $(x-2)$: \[ y = \frac{6}{x-2} \]

Step 4: Replace $y$ with $g^{-1}(x)$

Replace $y$ with $g^{-1}(x)$: \[ g^{-1}(x) = \frac{6}{x-2} \]

Final Answer The final answer is $\boxed{g^{-1}(x) = \frac{6}{x-2}}$

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