If q(x)=x+4, determine q(q(q(q(q(q(q(q(q(q(x^3)))))))))). [Hint: look for a pattern]

8 years ago

Answered By Tomokazu S

q(x)=x+4

q(x^{3})=x^{3}+4x1

q(q(x^{3}))=q(x^{3}+4)=x^{3}+8=x^{3}+4x2

q(q(q(x^{3})))=q(x^{3}+8)=x^{3}+12=x^{3}+4x3

Now you can see ten of q in the question.

Therefore the final answer is x^{3}+4x10=x^{3}+40.

8 years ago

Answered By Julius d

Given: q(x) = x + 4

Solve: q(q(q(q(q(q(q(q(q(q(x^{3}))))))))))

Solution: start from the innermost parenthesis.

q(x^{3}) = (x^{3}) + 4

q(q(x^{3})) = q(x^{3 }+ 4) = x^{3 }+ 4 + 4

Notice that the answer is an x^{3} and a bunch of +4's. The number of +4's is actually the same as the number of q's. Therefore for 10 q's (problem), the answer must be x^{3 }+ 4(10) which is equal to

x^{3} + 40

8 years ago

Answered By Jaehoon N

If q(x) = x+4,

q(x^{3}) = x^{3}+4 because the x^{3} replaces the x from x+4.

So using that concept,

for q(x^{3}+4)

The x^{3}+4 inside the bracket would replace the x from x+4 which would give you: q(x^{3}+4) = (x^{3}+4) +4

So you are now at q(q(q(q(q(q(q(q(x^{3}+8)))))))). The same thing applies for the rest of the equation, which you could simply recognize the arithmetic sequence of x^{3}+4(10) = x^{3}+40.

*10 is the number that is multiplied to the 4 because that is how many q(x)'s or functions are given in the question.*

8 years ago

Answered By Changliang Z

q(X)=X+4

q(x^3)=x^3+4

q(q(x^3))=(x^3+4)^3+4

.......

The final pattern is (((((((((x^3+4)^3+4)^3+4)^3+4)^3+4)^3+4)^3+4)^3+4)^3+4)^3+4

8 years ago

Answered By Changliang Z

My roommate said the answer should be x3+40. I think so.

He said here X=x^3, so I did not answer this question by X but x. Sorry

8 years ago

Answered By Victor Luis F

(g(x3)n=(10)^{n}(x3+4)

appliying log in both sides of the equation and afterwards returning with the power of 10 in both

sides of the equation

8 years ago

Answered By Victor Luis F

Sorry I will like to make a correction to my answer, the answer is the following:

8 years ago

## Answered By Tomokazu S

q(x)=x+4

q(x

^{3})=x^{3}+4x1q(q(x

^{3}))=q(x^{3}+4)=x^{3}+8=x^{3}+4x2q(q(q(x

^{3})))=q(x^{3}+8)=x^{3}+12=x^{3}+4x3Now you can see ten of q in the question.

Therefore the final answer is x

^{3}+4x10=x^{3}+40.8 years ago

## Answered By Julius d

Given: q(x) = x + 4

Solve: q(q(q(q(q(q(q(q(q(q(x

^{3}))))))))))Solution: start from the innermost parenthesis.

q(x

^{3}) = (x^{3}) + 4q(q(x

^{3})) = q(x^{3 }+ 4) = x^{3 }+ 4 + 4Notice that the answer is an x

^{3}and a bunch of +4's. The number of +4's is actually the same as the number of q's. Therefore for 10 q's (problem), the answer must be x^{3 }+ 4(10) which is equal tox

^{3}+ 408 years ago

## Answered By Jaehoon N

If q(x) = x+4,

q(x

^{3}) = x^{3}+4 because the x^{3}replaces the x from x+4.So using that concept,

for q(x

^{3}+4)The x

^{3}+4 inside the bracket would replace the x from x+4 which would give you: q(x^{3}+4) = (x^{3}+4) +4So you are now at q(q(q(q(q(q(q(q(x

^{3}+8)))))))). The same thing applies for the rest of the equation, which you could simply recognize the arithmetic sequence of x^{3}+4(10) = x^{3}+40.*10 is the number that is multiplied to the 4 because that is how many q(x)'s or functions are given in the question.*

8 years ago

## Answered By Changliang Z

q(X)=X+4

q(x^3)=x^3+4

q(q(x^3))=(x^3+4)^3+4

.......

The final pattern is (((((((((x^3+4)^3+4)^3+4)^3+4)^3+4)^3+4)^3+4)^3+4)^3+4)^3+4

8 years ago

## Answered By Changliang Z

My roommate said the answer should be x3+40. I think so.

He said here X=x^3, so I did not answer this question by X but x. Sorry

8 years ago

## Answered By Victor Luis F

(g(x3)n=(10)

^{n}(x3+4)appliying log in both sides of the equation and afterwards returning with the power of 10 in both

sides of the equation

8 years ago

## Answered By Victor Luis F

Sorry I will like to make a correction to my answer, the answer is the following:

g(x

^{3})=(x^{3}+4)^{n}