Function problem: If f(x)=(1/1-x) and g(x)=(1/x), find |[A B][C D]|...

[bobrossu]

Problem:

f(x)=(1/1-x) and g(x)=(1/x), find |^A_C ^B_D| if g(f(g(7))= (A/B) for relative prime positive integers A and B, and f(g(C/D))=(13/11) for relatively prime positive integers C and D.

The problem for me is understanding what to find.

the find |^A_C ^B_D| is supposed to have the line, then A above C, a space, then B above D and a line. They are not fractions.

 

[mmm4444bot]

f(x)=(1/(1-x)) and g(x)=(1/x), find |^A_C ^B_D| if g(f(g(7))= (A/B) for relative prime positive integers A and B, and f(g(C/D))=(13/11) for relatively prime positive integers C and D.

NOTE: The blue grouping symbols are unnecessary, and the added, red grouping symbols are required.

The problem for me is understanding what to find.

\(\displaystyle \begin{vmatrix} A & B \\ C & D \end{vmatrix} = A \cdot D - C \cdot B\)

This is the Determinant of a 2×2 Matrix.

First, you need to find the values of A, B, C, and D. Use the given function definitions and ratios for that.

Then, you need to find the value of the Determinant. Substitute your values into the right-hand side of the equation above. :cool:

 

[stapel]

Given f(x) = 1/(1-x) and g(x) = (1/x), find |^A_C ^B_D| if g(f(g(7)) = (A/B) for relative prime positive integers A and B, and f(g(C/D)) = (13/11) for relatively prime positive integers C and D.

The problem for me is understanding what to find. The "find |^A_C ^B_D|" is supposed to have the line, then A above C, a space, then B above D and a line. They are not fractions.

From what you've posted, it sounds as though you are being asked something about the "determinant" of a "matrix", but you haven't heard of these terms before. To learn what they are and how they work (since it seems that this is expected of you), you may want to attempt online self-study. (Warning: This could take anywhere from days to weeks.) To get started, turn to your favorite search engine and search for "matrix" (or "matrices", which is the plural of "matrix") and "determinants". You should be able to find plenty of resources to help you understand what is being asked of you.

Before the "find" part, you've got the algebra of functions. Are you okay on that part? Thank you!