How do you find the inverse of y=log_4( x/2 +3 )y=log4(x2+3)?

2 Answers
A. S. Adikesavan
Mar 7, 2016

x = 2(4^y-3)4y−3)

Explanation:

Raise both sides to the power of the base of the logarithm, 4
Use 4^log (x/2+3)4log(x2+3)= x/2+3x2+3...
4^y=x/2+34y=x2+3.

Noah G
Mar 12, 2016

The inverse of a function can be found algebraically by switching the x and y values and solving for y.

Explanation:

y = log_4(x/2 + 3)y=log4(x2+3)

x = log_4(y/2 + 3)x=log4(y2+3)

4^x = y/2 + 34x=y2+3

4^x - 3 = y/24x−3=y2

2(4^x - 6) = y2(4x−6)=y

2(4^x) - 12 = y2(4x)−12=y

So, f^-1(x) = 2(4^x) - 12f−1(x)=2(4x)−12. Note the f^-1(x)f−1(x): this is important because it shows efficiently and clearly that this is an inverse function. I have been docked marks before for not including this element in my answer.

Practice exercises:

  1. Find the equation of the inverse function.

a). g(x) =3^(x - 2) + 4g(x)=3x−2+4

b). h(x) =2 log_2(3x - 1)h(x)=2log2(3x−1)

Good luck!

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