How do you find the inverse of y=log_2(x+4)?

1 Answer
Jan 11, 2016

f^-1(x) = 2^x-2

Explanation:

For finding the inverse follow these steps.

Step 1: Swap x and y
Step 2: Solve for y
Step 3: Write the result in the correct notation.

To find inverse of y=log_2(x+4)

Step 1: Swap x and y

x=log_2(y+4)

Step 2: Solve for y

Convert the log to exponent form.
if log_b(a) = k then a=b^k

We have x=log_2(y+2)
2^x = y+2

Subtracting 2 on both the sides.
2^x-2 =y

y=2^x - 2 Inverse function

Step 3:

f^-1(x) = 2^x-2