SOLUTION: Let p(x) = 2x^3 - 113 and let q be the inverse of p. Find q(137). Please be sure to clearly explain your steps and support your arguments. This week we are particularly interested

Algebra.Com
Question 1089765: Let p(x) = 2x^3 - 113 and let q be the inverse of p. Find q(137). Please be sure to clearly explain your steps and support your arguments. This week we are particularly interested in your mathematical reasoning and rigor.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
p(x) = 2x^3 - 113 is shifted x^3.

    Therefore, it is one-to-one function over the entire domain  < x <  and maps the real number line by an one-to-one way onto itself.


To find the inverse function, express first x via p:

x = 


and then replace x by y and p by x. You will get the expression for the inverse function 

y = .     (1)


To calculate y(137), simply substitute 137 instead of x into the formula (1). You will get

y =  =  = 5.

Answer.  The value under the question is  5.



RELATED QUESTIONS

Let p(x) = 2x^3 - 113 and let q be the inverse of p. Find q(137). Please be sure to... (answered by ikleyn)
Let p/5 = Q then p/10= ? Please explain the steps that lead to the answer of:... (answered by Mathtut)
Recall that P3 is the space of all polynomials of degree less than three with real... (answered by khwang)
Let P and Q be polynomials such that P(x) and Q(P(Q(x))) have the same roots. If the... (answered by drk)
Let p, q, r, and s be the roots of g(x) = 3x^4 - 8x^3 + 5x^2 + 2x - 17 - 2x^4 + 10x^3 +... (answered by ikleyn)
Please Help. I'm so confused and lost with theese questions. 1. Write a negation of... (answered by amyd62)
construct a truth table q--->(p v~q). and be sure to includ all intermediate steps in... (answered by Edwin McCravy)
Let p, q, and r be the following statements: p: Roses are red q: The sky is blue... (answered by solver91311)
For all integers p and q, let # be defined by p # q = p^2 + q^2 + 2pq . Which of the... (answered by richard1234)