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
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-> 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
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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(52776) (Show Source):
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.
