How do you find the compositions given f(x)=8x-1 and g(x)=x/2?

2 Answers
Jan 7, 2016

g(f(x))=g@f=(8x-1)/2=4x-1/2
f(g(x))=f@g=8x/2-1=4x-1

Explanation:

You can think:
a)
y=f(x)=8x-1
z=g(y)=y/2
z=h(x)=g(f(x))=(8x-1)/2=4x-1/2

b)
y=g(x)=x/2
z=f(y)=8y-1
z=h(x)=f(g(x))=8x/2-1=4x-1

Remember that:

g@f!=f@g

Jan 7, 2016

Substitute the expression for g(x) in place of x in the definition of f(x) to find: (f@g)(x) = 4x-1

Similarly find: (g@f)(x) = 4x-1/2

Explanation:

(f@g)(x) = f(g(x)) = f(x/2) = 8(x/2)-1 = 4x-1

(g@f)(x) = g(f(x)) = g(8x-1) = ((8x-1))/2 = 4x-1/2