Solve f(x) = x^2, g(x) = x - 4, f(g(6))

Step by step, with the reason for every step · Composition and inverse functions · Algebra 2

Step by step

Question: find f(g(6)) for f(x) = x² and g(x) = x − 4.

f(x) = x²

g(x) = x − 4

f(g(6)) is a function inside a function.

Like with brackets, we start inside.

First g(6).

inside first: g(6)

Put 6 in place of x in g.

g(6) = 6 − 4

6 minus 4 is 2.

g(6) = 2

g(6) is 2.

So f(g(6)) is f(2).

f(g(6)) = f(2)

Put 2 in place of x in f.

= 2²

2² means 2 times 2.

2² = 2 × 2 = 4

That is 4.

f(g(6)) = 4

So f(g(6)) = 4.

Let's look back.

First: work out the inside.

Last: then the outside.

Answer

f(g(6)) = 4

Try this one yourself, then check:

f(x) = x², g(x) = x − 3, find f(g(6))

Show the answer

f(g(6)) = 9