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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]

:)

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