What is the quotient of the following rational expression? x^3+3x^2-4x+5/x^2-2
1 answer:
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Explanation:
<h3>Part 1.</h3>The inverse of a function y = f(x) can be found by solving x = f(y) for y.
When we do that here, we find ...
When we compare this to g(x), which we want to be the inverse of f(x), we see that ...
cx -d = bx -a ⇒ b=c, and d=a
We can choose a=d=1 and b=c=2 to make the two functions inverses:
f(x) = (x +1)/2
g(x) = 2x -1
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<h3>Part 2.</h3>The inverse of f(x) is g(x) if f(g(x)) = x.
f(g(x)) = ((2x -1) +1)/2 = 2x/1 = x . . . . . g is the inverse of f
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<h3>Part 3.</h3>Same as Part 2, but in reverse.
g(f(x)) = 2((x +1)/2) -1 = (x +1) -1 = x
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<h3>Part 4.</h3>The attachment is a graph of the two functions and a table of values. The line y=x is the dashed orange line. You will notice that f(x) and g(x) are reflections of each other across that line.
