How do you find the inverse of $y = {log}_{2} (x + 4)$ $y=log_2(x+4)$ ?

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Answer 1 · 2016-01-11T12:37:51

$f^{- 1} (x) = 2^{x} - 2$ $f^-1(x) = 2^x-2$

For finding the inverse follow these steps.

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

To find inverse of $y = {log}_{2} (x + 4)$ $y=log_2(x+4)$

Step 1: Swap $x$ $x$ and $y$ $y$

$x = {log}_{2} (y + 4)$ $x=log_2(y+4)$

Step 2: Solve for $y$ $y$

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:

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

How do you find the inverse of y=log_2(x+4)y=log2(x+4)y=log_2(x+4)?