Respuesta :

Hemo4

Answer: [tex]f^{-1} (x)=x^{2} -7[/tex]

Step-by-step explanation:

To find the inverse of a function replace f(x) with x and the original x with y

[tex]f(x)=\sqrt{x+7} \\x=\sqrt{y+7}[/tex]

Now we can solve for y

Square both sides so we can cancel out the root

[tex]x=\sqrt{y+7}\\x^{2} =\sqrt{y+7}^{2} \\x^{2} =y+7[/tex]

Now subtract 7 from both sides

[tex]x^{2} =y+7\\x^{2} -7=y+7-7\\x^{2} -7=y[/tex]

Now replace y with the inverse of f(x), [tex]f^{-1} (x)[/tex]

Answer:

f⁻¹=x²+7

Solution:

  • In order to find the inverse of a function, we should first replace f(x) with y, then switch x and y places, like so:
  • y=√x+7
  • x=√y+7
  • Now, solve the equation for y.
  • Square both sides in order to get rid of the square root:
  • x²+7=y
  • y=x²+7
  • And finally, replace y with f⁻¹:
  • f⁻¹=x²+7
  • Also, inverse functions do the opposite thing in the opposite order.
  • So if we have f(x)=x+7, the inverse function is: f⁻¹=x-7

Hope it helps.

Do comment if you have any query.

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