How do you find the inverse of #y=(x+3)²-5# and is it a function?

Answer 1
#y = (x + 3)^2 - 5#
#x = (y + 3)^2 - 5#
#x + 5 = (y + 3)^2#
#+-sqrt(x + 5) = y + 3#
#+-sqrt(x + 5) - 3 = y#
Hence, #y^(-1) = -3 +- sqrt(x + 5)#

This is not a function, since each value of x often has more than one corresponding value of y.

Hopefully this helps!

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Answer 2

To find the inverse of the function ( y = (x+3)^2 - 5 ), follow these steps:

  1. Replace ( y ) with ( x ) and ( x ) with ( y ).
  2. Solve the resulting equation for ( y ).
  3. If the inverse exists, express it in terms of ( y ).

The inverse of the given function is ( x = (y+3)^2 - 5 ).

To determine if this inverse is a function, check if it passes the vertical line test. If every vertical line intersects the graph at most once, then it is a function.

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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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