Inverse & Log property Review

Inverse

100

Find the inverse of { (2,6) (-3,7) (8,11) (-2,7) (6,2) (-3,14)

(6,2) (7,-3) (11,8) (7,-2) (2,6) (14,-3)

200

Does the inverse of { (2,6) (-3,7) (8,11) (-2,7) (6,2) (-3,14) represent a function? Explain.  You need more than a yes or no answer

yes because no two x values repeat

300

Does the inverse of { (2,6) (-3,7) (8,11) (-2,7) (6,2) (-3,14) represent a one to one function? Explain 

You need more than a yes or no answer

no because the y coordinate of 7 repeats in two ordered pairs

400

Which test is used to determine if the graph of a given function will have an inverse function?

horizontal line test

500

which test is used to determine if the graph of a given relation is a function?

Vertical line test

Inverse algebraically

100

Find the inverse of y= sqrt(x+9)

x = sqrt ( y+9)

x² =y+9 

y = x²-9

200

Find the inverse of y = sqrt (x) +6

x = sqrt (y) +6

x-6 = sqrt (y)

(x-6)² = y

300

Find the inverse of y = -5x/7 +3

x = -5y/7. +3

x-3 = -5y/7

7x -21 = -5y

y= - (7x-21)/5

400

Verify f(x) = x/2 + 8   and.  g(x) = 2x - 12 are inverses of each other

x = y/2 +8

x-8 = y/2

y = 2(x-8)

y =2x-16. which does not equal 2x -12

they are not inverses og other

500

A function and its inverse are symmetrical over the 

line ___________.  ( write the equation of the line)

y = x

Express as a single log

100

Express aa a single log expression: log₃7-log₃x

log₃(7/x)

200

Express aa a single log expression: 3lnx +2lny - 4lnz

ln(x³y²/z)

300

Express aa a single log expression: 1/2 log₅7 - 2log₅x

log₅(sqrt 7/x²)

400

Express aa a single log expression: log₂5+log₂x - log₂3

log₂ (5x/3)

500

Express aa a single log expression: 1+ 3log₄x

log₄4 + log₄x³

log₄ (4x³)

Expand the log

100

ln x²z⁵/y³

2lnx +5lnz - 3lny

200

ln (sqrt 3x)/7

ln (3x)^1/2- ln7

1/2[ln3 +lnx ]- ln7

1/2ln3 +1/2lnx - ln7

300

log₃ sqrt(x-2)

1/2log₃(x-2)

400

log 10x

log10 + logx

1+ logx

500

3/2lnx⁶-3/4lnx⁸

lnx^3/2x6- ln^3/4x8

lnx⁹-lnx⁶

ln x⁹/x⁶

lnx³​​​​

Evaluate

100

log1000

3

200

log_1/81(27)

log_1/81(27)=x

(1/81)^X = 27

3^-4x = 3³

-4x = 3 ; x= -3/4

300

ln e^-3

ln e^-3=x

e^x =e^-3

x=-3

400

log₇3

log₇3 = x

7^x=3     

log7^x= log3

xlog7 = log3

x = log3/log7

500

log₃ 1/81

log₃ 1/81=x

3^x = 1/81

3^x = 3^-4

x=-4