How do you find the inverse of #f(x)=3sqrt(x+2)#?

Answer 1

To find the inverse of ( f(x) = 3\sqrt{x + 2} ), follow these steps:

  1. Replace ( f(x) ) with ( y ): ( y = 3\sqrt{x + 2} ).
  2. Swap ( x ) and ( y ): ( x = 3\sqrt{y + 2} ).
  3. Solve for ( y ): [ x = 3\sqrt{y + 2} ] [ \frac{x}{3} = \sqrt{y + 2} ] [ \left(\frac{x}{3}\right)^2 = y + 2 ] [ \frac{x^2}{9} = y + 2 ] [ y = \frac{x^2}{9} - 2 ]

So, the inverse function of ( f(x) = 3\sqrt{x + 2} ) is ( f^{-1}(x) = \frac{x^2}{9} - 2 ).

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Answer 2

#x=y^2/9-2#

Since #f(x)=y#, you need to isolate #x# and express it in terms of #y#, while now you have written #y# in terms of #x#. So, here are the steps:
#y=3sqrt(x+2)#
#y/3 = sqrt(x+2)# (divided both members by #3#)
#y^2/9 = x+2# (squared both members)
#y^2/9-2 = x# (subtracted #2# from both terms)

And here we go!

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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