1314 2.6 Combinations of Functions; Composite Functions

We exclude from a functions domain real numbers that cause division by ____

zero

The function (fog) is found by replacing each occurrence of ___ in the equation for _____.

g(x), f with g(x)

Real numbers that result in a square root of a _______ _______ are excluded from a functions domain.

negative number

The domain of h(x)=1/x + 3/x+1 consists of all real numbers except 0 and -1, represented in interval notation as _______.

(-infinity, -1)U(-1,0)U(0,infinity)

If f(g(x))=3/g(x)-9 and g(x)=27/x, then 0 and ___ must be excluded from the domain of fog.

3

The notation fog, called the _____ of the function f with g, is defined by _______.

composition, (fog)(x)=f(g(x))

Find the domain of the function: f(x)=sq. root x-4 + sq. root x+13

- Contains sq. roots/ radicals - set the radicands >/= to zero - x-4>/=0, x-13>/=0 x=4,x=-13 Domain: [4,infinity)

Find the domain of the function: f(x)=sq. root of x-9

- function contains a square root - because only non-negative numbers have real sq. roots, the gty. under the radical sign, x-9 must be >/= 0 -x-9>/=0, x>/=9 Domain:[9,infinity)

What is the domain fo the function: f(x)=14(x-10)

(-infinity, infinity)

f(g(x))=f(x)*g(x)

False

The domain of g(x)=3 / x+7 consists of all real numbers except -7, represented in interval notation as _______.

(-infinity, -7)U(-7,infinity)

Find the domain fo the function: f(x)=12/x+8

(-infinity,-8)U(-8,infinity)

The domain of f(x)=9x+5 consists of all real numbers, represented in interval notation as ____.

(-infinity,infinity)

Find the domain of the function: f(x)=5/x^2+1 + 3/x^2-16

- No values of x^2+1 will be equal to zero - x^2-16 will have values that cause it to be zero (x+4)(x-4) x=-4, x=4 Domain: (-infinity,-4)U(-4,4)U(4,infinity)

The notation gof, called the _____ of the function g with f, is defined by ____.

composition, (gof)(x)=(g(f(x))

Find the domain of the function: f(x)=48/x^2+12x-63

This function contains division x^2+2x-63 = (x+9)(x-7)=0 x=-9 x=7 Domain: (-infinity,-9)U(-9,7)U(7,infinity)

fog is the same as function gof?

False

radicand

The number or expression inside a radical symbol