How do you write y=31+x2 as a composition of two simpler functions?

Define these functions: g(x)=1+x2 f(x)=3x Then: y(x)=f(g(x))

Explained: "How do you write y=31+x2 as a composition..."

Sereinserenormg

2022-01-25

How do you write

y = 3 \sqrt{1 + x^{2}}

as a composition of two simpler functions?

Jasmine Herman

Beginner2022-01-26Added 11 answers

Let

g (x)

be the first thing we do if we knew

x

and started to calculate:

g (x) = x^{2}

Now

f

will be the rest of the calculation we would do (after we found

x^{2}

)
It may be easier to think about if we gave

g (x)

a temporary name, say

g (x) = u

So we see that

y = 3 \sqrt{1 + u}

f (u) = 3 \sqrt{1 + u}

and that tells us we want:

f (x) = 3 \sqrt{1 + x}

Another answer is to letf

(x)

be the last thing we would do in calculating

y

.
So let

f (x) = 3 x

To get

y = f (g (x))

we need

3 g (x) = y

So let

g (x) = \sqrt{1 + x^{2}}

Kingston Gates

Beginner2022-01-27Added 8 answers

Define these functions:

g (x) = 1 + x^{2}

f (x) = 3 \sqrt{x}

Then:

y (x) = f (g (x))

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