Function Operations and Inverses

Function Operations

100

Find (f+g)(x) when, 

f(x) = 3x^2 - 4

g(x) = x^2 - 8x + 4

(f+g)(x)=4x^2 - 8x

200

Find (f-g)(x) when, 

f(x) = 3x^2 - 4

g(x) = x^2 - 8x + 4

(f-g)(x)=2x^2 + 8x - 8

300

Find (f x g)(x) when, 

f(x) = 3x^2 - 4

g(x) = x^2 - 8x + 4

(f x g)(x)= 3x^4 - 24x^3 + 8x^2 +32x - 16

400

If (f+g)(x) = x^2 -2x + 3, and f(x) = x^2 +1, then what is g(x)?

g(x) = -2x + 2

500

If (f - g)(x) = 2x^2 -x - 2, and f(x) = 2x^2 +1, then what is g(x)?

g(x) = -x - 3

Composition of Functions

100

Given the following functions, find g(h(x)).

f(x) = x^2 - 2x + 3

g(x) = x - 4

h(x) = 2x^2 - 5x - 6

g(h(x)) = 2x^2 - 5x - 10

200

Given the following functions, find g(h(0)).

f(x) = x^2 - 2x + 3

g(x) = x - 4

h(x) = 2x^2 - 5x - 6

g(h(0)) = -10

300

Given the following functions, find f(g(x)).

f(x) = x^2 - 2x + 3

g(x) = x - 4

h(x) = 2x^2 - 5x - 6

f(g(x)) = x^2 - 10x + 27

400

Given the following functions, find f(g(2)).

f(x) = x^2 - 2x + 3

g(x) = x - 4

h(x) = 2x^2 - 5x - 6

f(g(2)) = 11

500

Given the following functions, find g(2f(x)).

f(x) = x^2 - 2x + 3

g(x) = x - 4

h(x) = 2x^2 - 5x - 6

g(2f(x)) = 2x^2 - 4x + 2

Find the Inverse Function

100

Find the inverse of 

f(x) = x + 2

f^-1(x) = x - 2

200

Find the inverse of 

f(x) = (x-4) / 3

f^-1(x) = 3x + 4

300

Find the inverse of 

f(x) = x^2 + 3

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

400

Find the inverse of 

f(x) = sqrt(x-5) - 7

f^-1(x) = (x+7)^2 + 5

500

Find the inverse of 

f(x) = sqrt(2/3x)

f^-1(x) = 3/2x^2 

Verify the Inverse

100

Determine if the two functions are inverses of each other.

f(x) = 2x + 3

g(x) = 2x - 3

No

200

Determine if the two functions are inverses of each other.

f(x) = 4x + 6

g(x) = (x - 6) / 4

Yes

300

Determine if the two functions are inverses of each other.

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

g(x) = -3x + 9

Yes

400

Determine if the two functions are inverses of each other.

f(x) = (x + 6)^2

g(x) = sqrt(x) - 6

Yes.

500

Determine if the two functions are inverses of each other.

f(x) =  2sqrt(x - 5) 

g(x) = 1/4x^2 - 5

No.

Domain and Range

100

Determine the domain and range of the function.

f(x) = sqrt(6x)

D = {x | x >= 0}

R = {y | y >= 0}

200

Determine the domain and range of the function.

f(x) = sqrt(x + 2) + 5

D = {x | x >= -2}

R = {y | y >= 5}

300

Determine the domain and range of the function.

f(x) = sqrt(x-4) - 6

D = {x | x >= 4}

R = {y | y >= -6}

400

Determine the domain and range of the function.

f(x) = -sqrt(x-6) + 5

D = {x | x >= 6}

R = {y | y <= 5}

500

Determine the domain and range of the function.

f(x) = -3sqrt(x+7) + 9

D = {x | x >= -7}

R = {y | y <= 9}