composition of functions assignment

given: f(x)= x^2-3 & g(x)= x+1 the composite function g(f(x)) is

x^2-2

f(x)= x^2 +1

x^4 + 2x^2 +2

given: g(x)= sqrt x-4 & h(x)=2x-8 what is g(h(10))

2sqrt2

use the graph shown to evaluate the composition f(g(0))

3

Given: f(x) = 2x + 5 and g(x) = x^2 and h(x) = -2x h(g(f(x)))=

-8x^2+-40x+-50

the table shows values for the two functions f & g for different values of x what is f(g(0))

1

what is f(g(13))

32

given: f(x)= 1/x+5 & g(x)= x-2

x does not = -3

a circular oil spill continues to increase in size. the radius of the oil spill, in miles, is given by the function r(t) = 0.5 + 2t, where t is the time in hours. the area of the circular region is given by the function a(r) = πr2, where r is the radius of the circle at time t. explain how to write a composite function to find the area of the region at time t.

write the composition a compose r: a(r(t)) the function r(t) is the inside function, or inpit in function a(r) substitute 0.5 + 2t into the area formula in place of r: a(r(t))= pi((0.5+2t)^2

given: g(x)= sqrt x-4 & h(x)=2x-8 what are the restrictions on the domain of g(h)

x>=6