Student Question

Function

Determine whether the function f(x)=(2x-5)/(7x+4) has an inverse and , if so , find the inverse.

Expert Answers

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We see that for each value of x, f(x)=(2x-5)/(7x+4) has only one value and each value of f(x) can be obtained by only one value of x.

The function has an inverse.

Let y = f(x)=(2x-5)/(7x+4)

express x in terms of y

=> (7x + 4)y = 2x - 5

=> 7xy + 4y = 2x - 5

=> 7xy - 2x = -5 - 4y

=> x(7y - 2) = -5 - 4y

=> x = (5 + 4y)/(2 - 7y)

interchange x and y

=> y = (5 + 4x)/(2 - 7x)

The inverse function f^(-1)(x) = (5 + 4x)/(2 - 7x)

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