CPM Homework Help : CALC Problem 5-136

Find the inverse function, f ⁻¹ (x), for each of the following functions. Homework Help ✎
1. f(x) = log₃x
2. f(x) = 6²^x
3. f(x) = π²
4. f(x) = a^x + k

Steps (a):

Start by solving for x.
y = log₃x
x = 3^y
Now 'rename the x and y'.

Answer (a):

f ⁻¹(x) = 3^x

Hint (c):

Notice that y = π² is a horizontal line. What is the inverse of a horizontal line?

Steps (b):

y = 6²^x
2x = log₆y

$x=\frac{\text{log}_6y}{2}$

f ⁻¹(x) = ____________

Hint (d):

Refer to hint in part (b).

Hint (d):

Before you convert to a logarithm, subtract k from both sides.