Find the inverse of the function.
f(x) = 10^x + 2
f^(-1)(x) = (ln(x-2))/(ln(10))
or
f^-1(x) = log (x-2)
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)