## Ontario Free Tutoring And Homework Help For Math 12 University - Advanced Functions

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

6 years ago

q(x)=x+4

q(x3)=x3+4x1

q(q(x3))=q(x3+4)=x3+8=x3+4x2

q(q(q(x3)))=q(x3+8)=x3+12=x3+4x3

Now you can see ten of q in the question.

Therefore the final answer is x3+4x10=x3+40.

6 years ago

Given: q(x) = x + 4

Solve: q(q(q(q(q(q(q(q(q(q(x3))))))))))

Solution: start from the innermost parenthesis.

q(x3) = (x3) + 4

q(q(x3)) = q(x+ 4) = x+ 4 + 4

Notice that the answer is an x3 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+ 4(10) which is equal to

x3 + 40

6 years ago

If q(x) = x+4,

q(x3) = x3+4 because the x3 replaces the x from x+4.

So using that concept,

for q(x3+4)

The x3+4 inside the bracket would replace the x from x+4 which would give you: q(x3+4) = (x3+4) +4

So you are now at q(q(q(q(q(q(q(q(x3+8)))))))). The same thing applies for the rest of the equation, which you could simply recognize the arithmetic sequence of x3+4(10) = x3+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.*

6 years ago

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

6 years ago

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

6 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

6 years ago

#### Answered By Victor Luis F

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

g(x3)=(x3+4)n