Name: Composition of functions: solution walkthrough
Uploaded: 2026-11-13
Duration: 1 min 30 s
Description: Given f(x) = 13 - 2x and g(x) = x² + 1, what is the value of f(g(2))? Try it, then watch the animated solution.

Work from the inside out. In

f(g(2))

, the output of

g

becomes the input of

f

.

Inside first. Put

2

into

g

:

g(2) = 2^2 + 1 = 4 + 1 = 5

.

Replace

g(2)

with its value,

5

. Now

f(g(2))

is

f(5)

.

Put

5

into

f

:

f(5) = 13 - 2(5) = 13 - 10 = 3

.

Traps:

5

stops after

g

.

82

runs

f

first, then

g

.

45

multiplies

f(2)

by

g(2)

.

Try it first