Rational Exponents/Properties
convert to radical form. x2/3
CRTx2
Given f(x) = 5x, g(x) = x + 2, State the domain of (f/g)(x).
Domain: All Reals where x cannot be -2
(-inf, -2) U (-2, inf)
Looking at the tables. Are the following inverses?
A: (0,6) (1,2) (2,3) (-2,8) (5,0)
B: (6, 0) (2,1)(3,2) (8, -2) (0,5)
Yes!
Domain of y = (x) 1/2
[ 0, infinity)
Given (4x+9)1/2=5 Is x=4 a solution?
Yes. (4(4)+9)^(1/2)=5 (25)^(1/2)=5 5=5!
71/4 * 71/2
73/4 *Common base - add exponents
f(x) = 3x -8 and g(x) = 2x2. Find the following. g(f(5))
g(f(5)) = 98
bc. f(5) = 3(5) - 8 = 7 g(7) = 2(7)^2 = 2(49) = 98
Use the VLT and HLT on the graph of f(x) =x2. Is f(x) a function? Is f^-1 (x) a function?
f(x) is a function bc f(x) passes the VLT f-1 (x) is not a function bc f(x) does not pass HLT
State the domain & range. y = SQRT (x-2)
Domain: [2, infinity): Range [0, infinity)
Given x + 1 = (7x+15)1/2. Are both, one, or neither of the following solutions? x = 7 or x = -2
The only solution is x=7. x =-2 is extraneous.
(64y6 )1/3
4y2
f(x) = 4x-1 and g(x) = 5x - 2 Find f(f(x))
x
Find an equation for the inverse of the relation y =3x - 5
y = 1/3 x + 5/3 or y = (x+5)/3
State the Domain & Range. y = (x-3)1/2 + 2
Domain: [3, inf) Range [2, inf)
Solve (2x + 7)1/3 = 3.
x = 10
Find the inverse of f(x) = -10x6
f-1(x) = - ( x/-10)1/6
Graph y = sqrt(x-6)
see picture
Solve. x+1 = (7x + 15)1/2
x = 7
Simplify ((x+2)1/2 +1)2
x + 3 + 2(x+2)1/2