Step by step
The question
Question: find g(f(1)) for g(x) = 2x and f(x) = x + 5.
g(x) = 2x
f(x) = x + 5
1 Work out the inside
g(f(1)) is a function inside a function.
Like with brackets, we start inside.
First f(1).
inside first: f(1)
Put 1 in place of x in f.
f(1) = 1 + 5
1 plus 5 is 6.
f(1) = 6
2 Then the outside
f(1) is 6.
So g(f(1)) is g(6).
g(f(1)) = g(6)
Put 6 in place of x in g.
= 2(6)
2(6) = 2 × 6
2(6) means 2 times 6.
2 times 6 is 12.
g(f(1)) = 12
So g(f(1)) = 12.
Let's look back.
First: work out the inside.
Last: then the outside.
Answer
g(f(1)) = 12