CPM Homework Help : APCALC Problem 6-9

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Home > APCALC > Chapter 6 > Lesson 6.1.1 > Problem 6-9

6-9.

Write the equation of the inverse, $f ^{–1}(x)$ , for each of the following functions.

$f ( x ) = 2 ^ { x }$
Steps (a):
Solve for $x$ : $\log_2y=x$
Then 'switch' the input and the output.
Answer (a):
f⁻¹(x) = log₂x

$f ( x ) = \operatorname { log } _ { 3 } x$
Hint (b):
This is the reverse of part (a).

$f ( x ) = \operatorname { log } _ { e } x$
Hint (c):
Recall that e is a constant. (It's value is between $2$ and $3$ )
Answer (c):
$f^{ −1}\left(x\right) = e^{x}$

$f ( x ) = 5 \cdot 9 ^ { x }$
Hint (d):
Be sure to divide both sides by $5$ before you solve for $x$ .

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