1. 5 x2 + 4x + 7 25 + 3 = 28 1.6 Warm-Up Evaluate the compositions if:
f(x) = x + 2 g(x) = 3 h(x) = x2 + 3
1. f(g(x)) 2. h(f(x)) 3. h(f(g(x)))
f(3)
h(x + 2)
h(f(3))
f(x) = x + 2
h(x) = x2 + 3
h(3 + 2)
3 + 2
(x + 2)2 + 3
h(5)
52 + 3 5
x2 + 4x
x2 + 4x + 7
= 28

2. 1.6a Inverse Functions Objective –
Students will define one-to-one functions and use the horizontal line test.
Students will be able to solve problems involving inverse functions.
To be able to evaluate logarithmic functions.

3. 1.6a Inverse Functions
Definition: A function f is called one-to-one if it never takes on the same value twice; that is...
whenever
Horizontal Line Test: A function is one-to-one if and only if no horizontal line intersects its graph more than once

4. Solving for the Inverse
1.6a Inverse Functions
Solving for the Inverse
STEP 1 Switch the “y” and the “x” values.
STEP 2 Solve for “y”.

5. Answer: y -1 = -5x + 2 Example 1: Find the inverse of 10y +2x = 4
10x + 2y = 4
2y = -10x + 4
y = -5x + 2
Answer: y -1 = -5x + 2

6. Answer: y -1 = (-1/3)x + 2 Example 2: Find the inverse of y = -3x + 6
x = -3y + 6
x = -3y + 6
– –6
x – 6 = -3y
– –3
y = (-1/3)x + 2
Answer: y -1 = (-1/3)x + 2

7. y = x 5 x = y 5 Example 3: Find the inverse of the function: f(x) = x5

8. Find the Inverse Equation:
1.6 Classwork
Find the Inverse Equation:
Y = 2x + 3
y = x2 + 1
y = x3 – 1
f(x) = 1 x3
2x + 1
x + 3

9. 1.6 Homework
Pg :
(5-8, 17, 23-28) all

10. Logarithmic Functions
The Richter Scale
Magnitude +1
E E(30) E(30)2 E(30)3 E(30)4 E(30)5 E(30)6 E(30)7 E(30)8 E(30)9
energy released: x 30

11. Logarithmic Functions
DEFINITION OF LOGARITHM WITH BASE b
logby = x if and only if bx = y
The expression logby is read as “log base b of y.”

12. Example 4
Rewrite the logarithmic equation in exponential form.
log3 9 = b) log8 1 = 0 c) log5 (1/25) = -2
32 = 9
80 = 1
5(-2) = 1/25
Example 5
Evaluate the expression.
log b) log c) log6 ( 1/36 )
4 x = 64
3 x = 27
6 x = 1/36
x = -2
x = 3
x = 3

13. Properties of Logarithms
Objective – To be able to use properties of logarithms
State Standard – 11.0 Students will understand and use
simple laws of logarithms.
Product Property logb uv = logb u + logb v
Quotient Property logb (u/v) = logb u - logb v
Power Property logb un = n logb u
Properties of Logarithms

14. Example 2
Expand log5 2x 6
log5 2 + log5 x 6
log log5 x

15. Example 3 Condense: 2 log3 7 – 5 log3 x = log3 7 2 – log3 x 5

16. 1.6b Assignment
Pg. 76
35, 36, 39, and 40