Calculus
posted by Britt on .
Math questions, please help me? :(?
Find the composite functions f o g and g o f for the given functions.
f(x) = 10^x and g(x) = log x
State the domain and range for each:
f(x) = 4x + 1 and g(x) = x^2
f(x) = sin x and g(x) = x^2  x + 1
f(x) = 10^x and g(x) = log x
If f = {(2,1), (1,2), (0,6), (1,3), (2,1), (3,5), (4,0), (5,8)} and g = {(2,6), (1,5), (0,8), (1,3), (2,9), (3,9), (4,0), (5,2)}, then find f o g and g o f.
and how on earth would I figure this out?
By graphing the functions, determine the region where log2(x+3) > 2x.

(f◦g)(x) = f(g(x))
f(x) = 10^x, so
f(g) = 10^g = 10^(logx) = x
Similarly, g◦f = x
Note that 10^x and logx are inverse functions
domain for all polynomials is all reals
g(x) = x^2 has range y>=0
g(x) = x^2x+1 = (x1/2)^2 + 3/4 has range y >= 3/4
since 10^x and logx are inverses, and the range of 10^x is y>0, the domain of logx is x>0
When given actual pairs, just pug and chug
(f◦g)(2) = f(g(2)) = f(6) is undefined
(g◦f)(2) = g(f(2)) = g(1) = 5
and so on
Visit wolframalpha.com and enter
plot y=log2(x+3) and y=2x
to see the graphs. Note that the lower solution is not exactly 3, since log(0) is not defined.