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

Question

07-09-2021
Mathematics

Answered

IDNLearn.com is your reliable source for expert answers and community insights. Discover detailed and accurate answers to your questions from our knowledgeable and dedicated community members.

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

Sagot :

Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Thank you for choosing IDNLearn.com. We’re committed to providing accurate answers, so visit us again soon.

4. En El Juego De Dominó, Encuentra La Probabilidad De Que Al Levantar Una Ficha De Dominó:A. La Ficha Tenga Un Número De Puntos Mayor Que 9B. La Ficha Tenga Un

Which Type Of Care Is NOT Covered By Medicare?A. Hospital B. Hospice C. Long-term Care D. Respite

The Most Common Service Voltage For Small Commercial Loads Is:A. 120 Volts B. 240 Volts C. 480 Volts D. 600 Volts

QUESTION 2What Caused The International Financial System, Set Up At The End Of WWI, To Collapse?A. The Rise Of Hitler Led To An Economic Boycott By The Western

10. Diya Appeared In A Competitive Exam Containing 100 Questions In Which 3 Marks Are Given For Every Correct Answer, 1 Mark Is Deducted For Each Incorrect Answ

\begin{tabular}{|l|c|}\hline \multicolumn{2}{|c|}{\begin{tabular}{c} States With Same-Day \\Registration\end{tabular}} \\\hline 2008 & [tex]$71 \%$[/tex] \\

Which Statements Accurately Describe The Function [tex]f(x)=3(16)^{\frac{3}{4} X}[/tex]? Select Three Options.A. The Initial Value Is 3.B. The Domain Is [tex]x

Constable, Inc. Had The Following Transactions During 2022:Issued $225,000 Of Par Value Common Stock For Cash.Recorded And Paid Wages Expense Of $103,300.Acquir

How Are The Graphs Of The Functions [tex]f(x) = \sqrt{16} X[/tex] And [tex]g(x) = \sqrt[3]{64} X[/tex] Related?A. The Functions [tex]f(x)[/tex] And [tex]g(x)[/t

We Can Draw Three Inequivalent Lewis Structures For Dinitrogen Monoxide, [tex]$N_2O$[/tex]. The Concepts Of Formal Charge And Electronegativity Can Help Us Choo

LammettHashidn LammettHashidn · Answer 1 · 2021-09-07T11:26:31-04:00

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)

Sagot :

Other Questions