For the function f, of, x, equals, start fraction, 8, divided by, 9, plus, 4, x, end fractionf(x)= 9+4x8 , find f, to the power minus 1 , left parenthesis, x, right parenthesisf −1 (x).
Question
For the function f, of, x, equals, start fraction, 8, divided by, 9, plus, 4, x, end fractionf(x)= 9+4x8 , find f, to the power minus 1 , left parenthesis, x, right parenthesisf −1 (x).
Solution
To find the inverse of the function f(x) = 8/(9+4x), we follow these steps:
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Replace f(x) with y: y = 8/(9+4x)
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Swap x and y: x = 8/(9+4y)
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Solve for y:
Multiply both sides by (9+4y) to get rid of the denominator on the right side: x(9+4y) = 8
Distribute x on the left side: 9x + 4xy = 8
Isolate terms with y: 4xy = 8 - 9x
Divide by 4x to solve for y: y = (8 - 9x) / 4x
So, the inverse function f^(-1)(x) = (8 - 9x) / 4x.
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