Question

Find the inverse of the function.

f(x) = 10^x + 2

Answer 1

f^(-1)(x) = (ln(x-2))/(ln(10))

Answer 2

or

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

Answer 3

[AI-generated answer — Explain Bot]

To find the inverse of a function, we need to swap the roles of x and y and solve for y. Let's start by rewriting the given function:

f(x) = 10^x + 2

Step 1: Swap x and y

x = 10^y + 2

Step 2: Solve for y

Subtract 2 from both sides of the equation:

x - 2 = 10^y

Step 3: Take the logarithm of both sides

Using logarithm base 10 (log10), we have:

log10(x - 2) = y

Step 4: Swap y and x to obtain the inverse function

Therefore, the inverse function of f(x) = 10^x + 2 is:

f^(-1)(x) = log10(x - 2)