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How do you find the inverse of #g(x)= log_8(4 x+6)#?

Answer 1

Serenity Jones

To find the inverse of ( g(x) = \log_8(4x + 6) ), follow these steps:

Replace ( g(x) ) with ( y ): ( y = \log_8(4x + 6) ).
Swap the roles of ( x ) and ( y ), and solve for ( y ).
Rewrite the equation with ( x ) as the subject.

[ x = \log_8(4y + 6) ] [ 8^x = 4y + 6 ] [ 4y = 8^x - 6 ] [ y = \frac{8^x - 6}{4} ]

So, the inverse of ( g(x) = \log_8(4x + 6) ) is ( g^{-1}(x) = \frac{8^x - 6}{4} ).

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Answer 2

Elias Ackerman

I tried this:

I would first use the definition of log to write:

#4x+6=8^g(x)#

isolate #x#:

#4x=8^g(x)-6#

#x=(8^g(x)-6)/4#

so we can rewrite it as the inverse #f#:

#f(x)=(8^x-6)/4#

hope it helps!

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Answer 3

Sophie Adams

To find the inverse of ( g(x) = \log_8(4x + 6) ), switch the roles of ( x ) and ( y ), then solve for ( y ).

So, [ x = \log_8(4y + 6) ] [ 8^x = 4y + 6 ] [ 4y = 8^x - 6 ] [ y = \frac{8^x - 6}{4} ]

Therefore, the inverse function of ( g(x) ) is ( g^{-1}(x) = \frac{8^x - 6}{4} ).

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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.