dagmdesalegn0
Answered

Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

f(x)=ax+b/2 then f^-1 (x-1) =2x-5/2 find a and b​

Sagot :

LammettHash

From the given inverse function, we have

[tex]f^{-1}(x-1) = 2x - \dfrac52 \\\\ \implies f^{-1}(x) = f^{-1}((x+1)-1) = 2(x+1) - \dfrac52 = 2x-\dfrac12[/tex]

By definition of inverse function,

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

so that

[tex]f\left(2x-\dfrac12\right) = x[/tex]

[tex]a\left(2x-\dfrac12\right) + \dfrac b2 = x[/tex]

[tex]2ax - \dfrac a2 + \dfrac b2 = x[/tex]

[tex]\implies\begin{cases}2a=1 \\\\ -\dfrac a2+\dfrac b2 = 0\end{cases}[/tex]

[tex]\implies \boxed{a=\dfrac12}[/tex]

[tex]\implies \dfrac b2 = \dfrac a2 \implies \boxed{b=\dfrac12}[/tex]

Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.