Download 7.3 Power Functions & Function Operations

7.3
Power Functions & Function
Operations
Obj: add, subtract, multiply, and divide functions
Domain – all real x-values that “make sense”
(don’t include #s that will cause a zero in the
denominator and remember that you can’t take
the even nth root of a negative number)
Do
Not
Copy
Ex 1: Let f(x) = 3x1/3 & g(x) = 2x1/3
Find a) the sum
b) the difference
c) the domain for each
a) 3x1/3 + 2x1/3
= 5x1/3
b) 3x1/3 – 2x1/3
= x1/3
c) Domain of a is all real numbers
Domain of b is all real numbers
Ex 2: Let f(x) = 4x1/3 & g(x) = x1/2
Find a) the product
b) the quotient
c) the domain for each
a)
b)
4x1/3
4x
x
·
x1/2
= 4x1/3+1/2 = 4x5/6
1
3
*because you can’t take the 6th root of a
negative number.
= 4x1/3-1/2
= 4x-1/6
4
=
x
 x
5
c) Domain of a is all reals ≥ 0,
1
2
1
6
4
6
Domain of b is all reals > 0,

4
6
x
*because you can’t take the 6th root of a
negative number and you can’t have a
denominator of zero.
Ex 3: Let f(x) = 2x1/2 & g(x) = -6x1/2
Find the a) sum
b) difference
c) domain for each
Ex 4: Let f(x)=3x1/4 & g(x)=x1/3
Find the a) the product
b) the quotient
c) the domain for each
Day 2 Practice:
p.418 #14-26 evens
Note #7 continued…
4 - 1 - 09
Composition

f( g(x) ) means you take the function g
and plug it in for the x-values in the
function f, then simplify.

g( f(x) ) means you take the function f
and plug it in for the x-values in the
function g, then simplify.
Ex 5: Let f(x) = 2x-1 & g(x) = x2-1.
Find a) f(g(x))
b) g(f(x))
c) f(f(x))
d) the domain of a and b
a) 2(x2-1)-1 =
b) (2x-1)2-1
2
x2 1
c) 2(2x-1)-1
= 2(2-1x)
2x  x
=
2
= 22x-2-1
4
= 2 1
x
d) Domain of a all reals except x=±1
Domain of b all reals except x=0
Ex 6: Let f(x) = 3x-1 & g(x) = x2-4
Find
a) f( g(x) )
HW:
p.418
b) g( f(x) )
c) f( f(x) )
d) g( g(x) )
#28-38
Even
Notebook
check
tomorrow
e) the domain of a and b