Let s(x) = x^2 + 2x + 3xs(x)=x2+2x+3x and t(x) =sqrt( x+4)t(x)=√x+4 how do you find (s( t)) (6)(s(t))(6)?

2 Answers
F. Javier B.
Jun 1, 2018

See below for explanation

Explanation:

We have two functions and we have to compose them in the order to find s(t(6))s(t(6)). (The composition of functions is not conmutative)

We note that s(x)=x^2+5xs(x)=x2+5x

We proceed as follows

s(t(x))=s(sqrt(x+4))=(sqrt(x+4))^2+5sqrt(x+4)=x+4+5sqrt(x+4)s(t(x))=s(√x+4)=(√x+4)2+5√x+4=x+4+5√x+4

Then s(t(6))=6+4+5sqrt(6+4)=10+5sqrt10s(t(6))=6+4+5√6+4=10+5√10

A
Jun 1, 2018

s(t(6))= 10+5sqrt(10) s(t(6))=10+5√10
This question asks for s(t(6)) not s(t)(6)

Explanation:

To solve for s(t)(6)s(t)(6)
s(x) = x^2 +2x +3*x s(x)=x2+2x+3⋅x
t(x) = sqrt(x+4)t(x)=√x+4
let's first find s(t).
Substitute t(x) into s(x):
s(t(x))= (sqrt(x + 4))^2 +2sqrt(x+4)+3*sqrt(x+4)s(t(x))=(√x+4)2+2√x+4+3⋅√x+4
Simplifying this gives us:
s(t(x))= ( x + 4)+2sqrt(x+4)+3*sqrt(x+4)s(t(x))=(x+4)+2√x+4+3⋅√x+4
Now, subbing 6 into the X values gives us:
s(t(6))= ( 6+ 4)+2sqrt(6+4)+3*sqrt(6+4)s(t(6))=(6+4)+2√6+4+3⋅√6+4
s(t(6))= 10+2sqrt(10)+3*sqrt(10) s(t(6))=10+2√10+3⋅√10
s(t(6))= 10+5sqrt(10) s(t(6))=10+5√10

Additional info:
Note that functions like s(t(x)) are called composite functions.

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