Inverse Functions

Find the Inverse

100

What is the inverse of 

f(x)=x/4

What is 

4x

200

What is the inverse of 

f(x)=3x+1

What is

f^-1(x)=(x-1)/3

300

What is the inverse of 

j(x)=(2x+3)/4

What is 

j^-1(x)=2x-3/2

400

The inverse of 

g(x)=(8-5x)

What is 

g^-1(x)=(8-x)/5

g^-1(x)= (-x+8)/5

500

What is the inverse of 

g(x)=1/2(x-6)

What is 

g^-1(x)=2x+6

Are they really inverses?

100

f(x)=(x-5)/10

h(x)=10x+5

What is Yes

200

f(x)=3(x-9)

g(x)=1/3x+9

What is Yes

300

f(x)=x+10

g(x)=-x-10

No

400

g(x)=(8+9x)/2

f(x)=(5x-9)/2

What is No

500

f(x)=2x+2

g(x)=2x-2

No

Inverse Fun Facts

100

The inverse notation for the function 

f(x)

What is 

f^-1(x)

200

The graph of a function that passes through the point (-3,4). What point must lie on the graph of the function's inverse?

What is (4,-3)

300

True or false: a function and its inverse can never intersect

What is false

Example: 

f(x)=2x, f^-1(x)=x/2

400

When given the domain and range of a function but not the actual function, what information do I know about the inverse function?

What is the domain and range of my inverse function by interchanging x & y

500

True or false: a function can be its own inverse

What is true

Examples: 

y=x, y=-x+3

Composite Function

100

Is f(g(x)) the same as g(f(x))?

What is no

200

Find 

f(g(x))

f(x)=4x

g(x)=2x+7

What is 8x+28

300

Find

g(f(x))

f(x)=4x

g(x)= 2x+7

What is 8x+7

400

Find

f(g(x))

f(x)=x/4

g(x)=3x+1

  

What is (3x+1)/4

500

Find

fg(1)

f(x)=x/4

g(x)=3x+1

What is 

1