Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Our Q&A platform provides quick and trustworthy answers to your questions from experienced professionals in different areas of expertise. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

find f^(-1)for the function f(x)= (1)/(x+2)

Sagot :

LammettHash

If [tex]f(x)[/tex] and [tex]f^{-1}(x)[/tex] are inverses of each other, then we have

[tex]f\left(f^{-1}(x)\right) = x[/tex]

Since [tex]f(x) = \frac1{x+2}[/tex], we have

[tex]f\left(f^{-1}(x)\right) = \dfrac1{f^{-1}(x)+2} = x[/tex]

Solve for [tex]f^{-1}(x)[/tex] :

[tex]\dfrac1{f^{-1}(x)+2} = x \\\\ 1 = x\left(f^{-1}(x)+2\right) \\\\ 1 = x f^{-1}(x) + 2x \\\\ x f^{-1}(x) = 1 - 2x \\\\ f^{-1}(x) = \dfrac{1-2x}x \\\\ \boxed{f^{-1}(x) = \dfrac1x - 2}[/tex]

(provided that x ≠ 0 and x ≠ -2)

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.