Composing functions, step by step
f(g(2)) means work g(2) first, then feed its answer into f.
The question
Find f(g(5)).
f(x) = −2x − 5, g(x) = −4x − 5; f(g(5))
f(x) = −2x − 5
g(x) = −4x − 5
g(5)=−25
f(−25)=45
f(g(5))=45
- f(g(5)) means work the inside first: find g(5), then put THAT answer into f.
- g(5): multiply first, −4 × 5 = −20, then −20 − 5 = −25.
- Now put −25 into f: −2 × (−25) = 50, then 50 − 5 = 45.
- So f(g(5)) = 45.
How it works.
- 01
f(g(5)) means work the inside first: find g(5), then put THAT answer into f.
- 02
g(5): multiply first, −4 × 5 = −20, then −20 − 5 = −25.
- 03
Now put −25 into f: −2 × (−25) = 50, then 50 − 5 = 45.
- 04
So f(g(5)) = 45.