Find the inverse of the one-to-one function.
f(x)= (2x+5)/7
7 x = 2 y + 5
2 y = 7 x - 5
y = (7x-5)/2
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To find the inverse of a one-to-one function, we need to swap the roles of x and y and solve for y.
Let's start by swapping the x and y in the given function:
x = (2y + 5)/7
Next, we will solve this equation for y:
Multiply both sides of the equation by 7:
7x = 2y + 5
Subtract 5 from both sides of the equation:
7x - 5 = 2y
Divide both sides of the equation by 2:
(7x - 5)/2 = y
Therefore, the inverse function of f(x) = (2x + 5)/7 is:
f^(-1)(x) = (7x - 5)/2