Lesson 5 Inverse Universe Practice Understanding

Ready

Use properties of exponents to rewrite the expressions. Write your answers in exponential form with positive exponents.

1.

$\sqrt[7]{x^{2}} \cdot \sqrt[7]{x^{3}}$

2.

$\sqrt[3]{x} \cdot \sqrt[4]{x} \cdot \sqrt[6]{x}$

3.

$\sqrt[6]{a} \cdot \sqrt[3]{a^{2}} \cdot \sqrt[5]{b^{3}}$

4.

$\sqrt[5]{32} \cdot \sqrt{9} \cdot \sqrt[3]{27}$

5.

$\sqrt[4]{8} \cdot \sqrt[3]{16} \cdot \sqrt[6]{2}$

6.

${(5^{2})}^{3}$

7.

${(7^{2})}^{- 1}$

8.

${(3^{- 4})}^{- 5}$

9.

${(\frac{5^{- 4}}{5^{2}})}^{3}$

Set

Write the inverse of the given function with the same representation as the given function.

10.

Function $f (x)$ :

$x$	$f (x)$
$- 8$	$0$
$- 4$	$3$
$0$	$6$
$4$	$9$
$8$	$12$

Inverse $f^{- 1} (x)$ :

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

11.

Function $f (x)$ :

Inverse $f^{- 1} (x)$ :

12.

Function $f (x)$ : $f (x) = - 2 x + 4$

Inverse $f^{- 1} (x)$ :

13.

Function $f (x)$ :

Inverse $f^{- 1} (x)$ :

14.

Function $f (x)$ : $f (x) = 13 - x$

Inverse $f^{- 1} (x)$ :

15.

Function $f (x)$ :

$x$	$f (x)$
$0$	$0$
$1$	$1$
$2$	$4$
$3$	$9$
$4$	$16$

Inverse $f^{- 1} (x)$ :

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

Go

Calculate $f (g (x))$ and $g (f (x))$ for each pair of functions.

16.

$f (x) = 3 x + 7$ ; $g (x) = - 4 x - 11$

17.

$f (x) = - 4 x + 60$ ; $g (x) = - \frac{1}{4} x + 15$

18.

$f (x) = 10 x - 5$ ; $g (x) = \frac{2}{5} x + 3$

19.

$f (x) = - \frac{2}{3} x + 4$ ; $g (x) = - \frac{3}{2} x + 6$

20.

Look back at your calculations for $f (g (x))$ and $g (f (x))$ . Two of the pairs of equations are inverses of each other. Which pairs do you think they are?

Why?