Rational Exponents
Composition of Functions
Inverse Functions
Function Operation
Solving Radical Equations
100
Simplify
sqrt(16x^4y^12)
4x2y6
100
Find
fcircg
f(x) = 3x - 4
g(x) = 5x2
15x2-4
100
Find the inverse
y = 3x + 8
f^-1(x)=(x-8)/3
100
Find (f + g)
f(x) = x2 + 5x - 1
g(x) = -x - 3
x2 + 4x - 4
100
Solve
(x+5)1/2 = 3
x = 4
200
Simplify
sqrt(x^2y^3)*sqrt(x^4y^5)
x3y4
200
Find gcircf
f(x) = -x2 - 2x
g(x) = -2x - 5
2x^2+4x-5
200
Find the inverse
y = x2 - 1
f^-1(x)=sqrt(x+1)
200
Find (f - g)
f(x) = 7 - x2
g(x) = x2 - 4
-2x2 + 11
200
Solve
(x-7)1/2 - 3 = 4
x = 56
300
Simplify
5sqrt(7)-2sqrt(175)
-5sqrt(7)
300
Find f*g
f(x) = x2 - 2x
g(x) = x - 7
x^3-9x^2+14x
300
Does the following function have an inverse? Why?
Yes, because it passes the horizontal line test.
300
Find (fg)(x)
f(x) = -4x - 1
g(x) = 2x2 - x
-8x3 + 2x2 + x
300
Solve
sqrt(3x-2)+4=6
x = 2
400
Simplify
sqrt(48a^8)/sqrt(16a^2)
a^2sqrt(3)
400
Find f-g
f(x) = 6x - 3
g(x) = x - 3
5x
400
Find the inverse. Do not multiply, leave in parenthesis.
f(x)=root(3)(x+2)-4
f^-1(x)=(x+4)^3-2
400
Find (f/g)(x)
f(x) = (x - 2)1/2
g(x) = x / (x + 11)
[(x + 11)(x - 2)1/2] / x
400
Solve
-3root(3)(2-3x)-2 = 1
x = 1
500
Simplify
(5sqrt(11)+2)(2sqrt(11)+5)
120+29sqrt(11)
500
Find (fcircg)(9)
f(x) = x2
g(x) = x2+4
7225
500
Find the inverse
f(x)=sqrt(3+x)
f^-1(x)=x^2-3
500
Find (4f - 5g)(x)
f(x) = 9x - 1
g(x) = 5x2 - x - 2
-25x2 + 41x + 6
500
Solve.
root(3)(x^2 +5x +3)-7=-4
x = -1