Given the one-to-one function f(x)= 7x - 2, find it's inverse function.

Question

(A.) Given the one-to-one function f(x)= 7x - 2, find it's inverse function.

Which is f ^ -1(x)= 1/7x - 2/7

(B.) The graphs of f and f^ -1 are symmetric with respect to the line defined by

y = _______

Answer 1

y = 7x - 2

Switch x and y to get x = 7y - 2

Solve for y: y = (x + 2) / 7 = f^-1(x)

The graphs of f(x) and f^-1(x) are symmetric with respect to the line y = x.