if f(x)=5x+1 and g(x)=4/x. find f(g(x)) and g(f(x)).

Answer 1

f(x) = 5x+1

g(x) = (4/x)

f(g(x) = 5 g(x) + 1 = 5(4/x) + 1 = 20/x + 1

g(f(x) = 4/(f(x)) = 4/(5x+1)

Answer 2

f(x) = 5x+1 and g(x) = 4/x

when they say find f(g(x)) that means treat all x in f(x) as if those x = g(x) so if in f(x), x = g(x) = 4/x that means f(g(x)) = 5*(4/x)+1 = ((5*4)/x)+1 = (20/x) + 1

Then for g(f(x)) we use the same method so in g(x), x = 5x+1 thus g(f(x)) = 4/(5x+1) and there you go. you are just taking one function and putting it into another function.