Algebra help, collage level

Question

1. Given that f(x) = 2x+3 and g(x)=x^2-4x-6, find (g o f) 6
2. for the given function, find (f o g)(x) and (g o f)(x) and the domain and range of each

f(x)= sqrt x+6, g(x)= x^2-6

1. for the given functions, find (f o g)(x) and (g o f)(x) and the domain of each

f(x) 1-x/8x, g(x) 1/1+8x

((they are factions... just wanted to clarify))

please help me i have been trying these problems all day and I feel stupid and I need help... i just wanna get these solved already

Answer 1

Hey Brian

Just to get you started...

(f o g)x is the same thing as f(g(x)) which is a little easier to understand

you input the value of x in function g() then use the RESULT of that to input in the function f() rather than x

DOMAIN is every possible value you can input in a function. RANGE is every value you can get out.

With a "Composite" Function, The DOMAIN of the function f is all the values that function g can supply (the RANGE of g). The RANGE of function f() will be all the values the RESULT can be.

For example if the g() function always results in a positive value, then the only numbers that can be input into function f() are positive numbers. Even though function f() by itself COULD normally use Negative numbers, g() will never give it any. So the DOMAIN of f() is only what g() can supply and the results are only those numbers that putting Positive numbers in will give.

Hope this gives you something to work with.

Thomas H.