Composition of Functions
Describe what this means
f(g(x))
Acceptable Answers:
- function within a function
- input of g(x) into f(x)
- "f of g of x"
Let
(f+g)(x)=sqrt(4x+1)
Find
(f+g)(6)
(f+g)(6)=5
Let
(f-g)(x)=root(3)(4x-4)
Find
(f-g)(3)
(f-g)(3)=2
Let
(f*g)(x)=x^3+x
Find
(f*g)(3)
(f*g)(3)=30
Let
(f/g)(x)=(x+12)/(x)
Find
(f/g)(3)
(f/g)(3)=5
Let
f(x)=sqrt(x)
and
g(x)=x+1
Find
(f(g(x))
f(g(x))=sqrt(x+1)
Let
f(x)=5x
and
g(x)=x+2
Find
(f+g)(x)
(f+g)(x)=6x+2
Let
f(x)=5x
and
g(x)=x+2
Find
(f-g)(x)
(f-g)(x)=4x-2
Let
f(x)=5x
and
g(x)=x+2
Find
(f*g)(x)
(f+g)(x)=5x^2+10x
Let
f(x)=5x
and
g(x)=x+2
Find
(f/g)(x)
(f+g)(x)=(5x)/(x+2)
Let
f(x)=3x
and
g(x)=x+1
Find
(f(g(x))
f(g(x))=3x+3
Let
f(x)=7root(3)(x)
and
g(x)=-2root(3)(x)
Find
(f+g)(x)
(f+g)(x)=5root(3)(x)
Let
f(x)=7root(3)(x)
and
g(x)=-2root(3)(x)
Find
(f-g)(x)
(f-g)(x)=9root(3)(x)
Let
f(x)=x^4
and
g(x)=3sqrt(x)
Find
(f*g)(x)
(f*g)(x)=3x^(9/2)
Let
f(x)=x
and
g(x)=9sqrt(x)
Find
(f/g)(x)
(f/g)(x)=x^(1/2)/9
Let
f(x)=3x^2+5x
and
g(x)=x^3
Find
(f(g(x))
(f(g(x))=3x^6+5x^3
Let
f(x)=-7x^3+4x
and
g(x)=3x^3-2x+1
Find
(f+g)(x)
(f+g)(x)=-4x^3+2x+1
Let
f(x)=-7x^3+4x
and
g(x)=3x^3-2x+1
Find
(f-g)(x)
(f-g)(x)=-10x^3+6x-1
Let
f(x)=11x^3
and
g(x)=7x^(7/3)
Find
(f*g)(x)
(f*g)(x)=77x^(16/3)
Let
f(x)=-14x^(2/3)
and
g(x)=7x^(1/3)
Find
(f/g)(x)
(f/g)(x)=-2x^(1/3)
Let
f(x)=5x^2+2
and
g(x)=x+1
Find
(g(f(x))
(g(f(x))=5x^2+3
Let
f(x)=x^3-3x-1
and
g(x)=-3x^3-x+2
Find
(f+g)(-1)
(f+g)(x)=-2x^3-4x+1
(f+g)(-1)=7
Let
f(x)=x^3-3x-1
and
g(x)=-3x^3-x+2
Find
(f-g)(-1)
(f-g)(x)=4x^3-2x-3
(f-g)(-1)=-5
Let
f(x)=4x^(5/4)
and
g(x)=2x^(1/2)
Find
(f*g)(16)
(f*g)(x)=8x^(7/4)
(f*g)(16)=1024
Let
f(x)=4x^(5/4)
and
g(x)=2x^(1/2)
Find
(f/g)(16)
(f/g)(x)=2x^(3/4)
(f/g)(16)=16