x+2 you want to help Jenny solve the problem so what is the answer? ...

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PROBLEM:

Jenny is having a hard time getting the range of the function f(x) = 3/x+2. You want to help Jenny solve the problem so what is the answer?

ANSWER:

Let's first get the inverse of the function.

$\begin{array}{l} \sf f(x) = \frac{3}{x + 2} \\ \sf y = \frac{3}{x + 2} \\ \sf x = \frac{3}{y + 2} \\ \sf x(y + 2) = 3 \\ \sf xy + 2x = 3 \\ \sf xy = 3 - 2x \\ \sf y = \frac{3 - 2x}{x} \\ \sf f^{ - 1}(x)= \frac{3 - 2x}{x}\end{array}$

Then, let's find the domain of the inverse function.

$\begin{array}{l} \sf f^{ - 1}(x)= \frac{3 - 2x}{x} \\ \sf \frac{3x - 2}{x}; \: x \in R \: \{except \: 0 \} \\ \: \: \: \: \: \sf \: x ;\: x \in R \end{array}$