Math Analysis Honors – Worksheet 34
Inverse Functions and Graphs of Logarithmic Functions
Find the inverse of each function. State the domain of f. Label the inverse as g.
4
2x − 3
1) f ( x ) = 4x + 2
2) f ( x ) =
3) f ( x ) =
x+2
x+4
4) f ( x ) =
−2x
x −1
5) Use f and g from #2 and evaluate f ( g ( x )) and g ( f ( x )) . You should get the same answer for both.
Evaluate without using a calculator
6) log 3 9
7) ln e 3
8) ln
Graph each function.
i. State the domain.
ii. Identify any asymptotes
iii. Describe the end behavior
iv. Verify your graph with a graphing calculator.
10) f ( x ) = ln ( x − 3)
11) f ( x ) = e x−1
12) f ( x ) = 2 + ln x
x
14) f ( x ) = e 2
15) f ( x ) = e x − 3
1
e
16) f ( x ) = log ( x + 5 )
9) log 2 4 log2 8
13) g ( x ) = −2 ln x
⎛ x⎞
17) f ( x ) = log ⎜ ⎟
⎝ 2⎠