How do you find the inverse of #y=log( -3x) +2#?

Answer 1

To find the inverse of ( y = \log(-3x) + 2 ), follow these steps:

  1. Replace ( y ) with ( x ) and ( x ) with ( y ).
  2. Solve for ( y ).

So, the inverse function is ( x = \log(-3y) + 2 ). To solve for ( y ), first isolate the logarithmic term, then take the exponential of both sides.

Here's the process:

  1. Subtract 2 from both sides to isolate the logarithmic term: ( x - 2 = \log(-3y) ).
  2. Rewrite the equation in exponential form: ( -3y = 10^{x - 2} ).
  3. Divide both sides by -3: ( y = -\frac{1}{3} \cdot 10^{x - 2} ).

So, the inverse function is ( y = -\frac{1}{3} \cdot 10^{x - 2} ).

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Answer 2

#color(blue)(y=(-10^(x-2))/3)#

Have you have used the word 'log' I am assuming you are talking about #log_10#

Given:#" "y=log(-3x)+2#

#=> log(-3x)=y-2#

Note that #log(a)=b" "->" "10^b=a#

#=>log(-3x)=y-2" "->" "10^(y-2)=-3x#

#x=(-10^(y-2))/3#

Now swap the letters #x" and "y# around giving:

#color(blue)(y=(-10^(x-2))/3)#

#color(green)("This should be a reflection of the original equation about "#
#color(green)(y=x)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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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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