Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

f(x)=x^2-6. find the inverse

Sagot :

Answer:

f-1(x) = +- sqrt(x + 6)

Step-by-step explanation:

f(x) = x^2 - 6

y = x^2 - 6


x = y^2 - 6

x + 6 = y^2

y = +- sqrt(x + 6)

f-1(x) = +- sqrt(x + 6)

Eliza3038269

Hi :)

Let's find the inverse of the function

——————————

Remember, inverse functions do the opposite things in the opposite order.

To find the inverse,

  • replace [tex]\boldsymbol{f(x)}[/tex] with [tex]\boldsymbol{y}[/tex]
  • swap x's and y's
  • solve for y

Replace f(x) with y. (one step)

Then

[tex]\boldsymbol{y=x^2+6}[/tex]

Swap x's and y's (one step)

Then

[tex]\boldsymbol{x=y^2+6}[/tex]

Solve for y (several steps)

[tex]\boldsymbol{x-6=y^2}[/tex] > square root both sides

[tex]\boldsymbol{\sqrt{x-6}=y}[/tex] > swap y and √x-6

[tex]\boldsymbol{y=\sqrt{x-6}}[/tex]

[tex]\tt{Learn~More;Work~Harder}[/tex]

:)

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.