How do you find the compositions given f(x)=8x−1 and g(x)=x2?

2 Answers
Lucio Falabella
Jan 7, 2016

g(f(x))=g∘f=8x−12=4x−12
f(g(x))=f∘g=8x2−1=4x−1

Explanation:

You can think:
a)
y=f(x)=8x−1
z=g(y)=y2
z=h(x)=g(f(x))=8x−12=4x−12

b)
y=g(x)=x2
z=f(y)=8y−1
z=h(x)=f(g(x))=8x2−1=4x−1

Remember that:

g∘f≠f∘g

George C.
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−12

Explanation:

(f∘g)(x)=f(g(x))=f(x2)=8(x2)−1=4x−1

(g∘f)(x)=g(f(x))=g(8x−1)=(8x−1)2=4x−12

Related questions
See all questions in Function Composition
Impact of this question
2066 views around the world
You can reuse this answer
Creative Commons License