question\n\nfor the function $f(x) = \\frac{8}{9+4x}$, find $f^{-1}(x)$.\n\nanswer attempt 1 out of…
question\n\nfor the function $f(x) = \\frac{8}{9+4x}$, find $f^{-1}(x)$.\n\nanswer attempt 1 out of 2\n\n$f^{-1}(x) =$
Answer
Explanation:
Step1: Replace $f(x)$ with $y$
$$y = \frac{8}{9 + 4x}$$
Step2: Swap $x$ and $y$ to find inverse
$$x = \frac{8}{9 + 4y}$$
Step3: Multiply both sides by the denominator
$$x(9 + 4y) = 8$$
Step4: Distribute $x$ into the parentheses
$$9x + 4xy = 8$$
Step5: Isolate the term containing $y$
$$4xy = 8 - 9x$$
Step6: Solve for $y$ by dividing by $4x$
$$y = \frac{8 - 9x}{4x}$$
Step7: Replace $y$ with $f^{-1}(x)$
$$f^{-1}(x) = \frac{8 - 9x}{4x}$$
Answer:
f^{-1}(x) = \frac{8 - 9x}{4x}