Algebra 2 Function Operation & Inverse Review

Numerical Values

100

Find

(g-f)(1)

 when 

f(x) = 3x-2  :   g(x) = x² + 3x +10

13

200

Find

(f+g)(-4)

 when 

f(x) = 3x-2  :   g(x) = x²   :   h(x) = -4x³-x

2

300

Find g(f(-2)) when 

f(x) = 3x - 2  :   g(x) = x² - 4

g(f(-2)) = 60

400

Find g(f^-1(-11)) when 

f(x) = 3x - 2  :   g(x) = x² - 4

g(f^-1(-11)) = 5

500

Find h(f^-1(g^-1(x))) when 

f(x) = 0.5x + 4  :   g(x) = 4x - 10  :   h(x) = 2x³- x

h(f^-1(g^-1(x)))=124

Inverses

100

Find the inverse of the function

f(x) = 2x+4

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

200

Find the inverse of the function with domain x>0

f(x) = 1/2x^4 

f^(-1)(x) = root(4)(2x)

300

Find the inverse of the function

f(x) = x^3+5

f^(-1)(x) = root(3)(x-5)

400

Are the following functions inverses?

f(x) = 0.5x - 2    :   g(x) = -0.5x + 2

No, they are inverses as 

f(g(x)) and g(f(x)) do not equal x.

500

Are the following functions inverses?

f(x) = x³ + 8   :   g(x) = (x - 8)^1/3

Yes, they are inverses as 

f(g(x)) = g(f(x)) = x.

Function Operations and Composition

100

Find

g(x)-f(x)

 when 

f(x) = 3x-2  :   g(x) = x² + 3x +10

g(x)-f(x)=x^2+12 

200

Find f(f(x)) when 

f(x) = 3x-2  :   g(x) = x²   :   h(x) = -4x³-x

f(f(x)) = 9x-8

300

Find

f(x) *g(x)

 when 

f(x) = 3x-2  :   g(x) = x²   :   h(x) = -4x³-x

f(x)*g(x) = 3x^3-2x^2

400

Find g(f(x)) when 

f(x) = 3x-2  :   g(x) = x²-4

g(f(x))=9x^2-12x

500

Find f(g(h(x))) if

f(x) = 2x+1:&: g(x) = x^2+1 :&: h(x)=x+1

f(g(h(x)))= 2x^2+4x+5