Question

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

Answer 1

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

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)

Answer 2

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
  `\boldsymbol{f(x)}` with
  `\boldsymbol{y}`
• swap x's and y's
• solve for y

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

Then

`\boldsymbol{y=x^2+6}`

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

Then

`\boldsymbol{x=y^2+6}`

Solve for y (several steps)

`\boldsymbol{x-6=y^2}` > square root both sides

`\boldsymbol{√(x-6)=y}` > swap y and √x-6

`\boldsymbol{y=√(x-6)}`

`\tt{Learn~More;Work~Harder}`

:)