Given the one-to-one function f(x)= 7x - 2, find it's inverse function. The graphs of f and f^ -1 are symmetric with respect to the line defined by

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 and solve for the new y

x = 7y -2

7y =x+2

y = f^-1(x) = (x+2)/7 = the inverse function, the one to one inverse function symmetric about y=x

or f^-1(x) = x/7 + 2/7

Answer 2

(A) f(x) = 7x - 2 *Given.

y = 7x - 2 *Change the f(x) to y.

x = 7y -2 *Switch the x and y in the equation because the range of the function = the domain of

the inverse and the domain of the function = the range of the inverse.

y = 1/7 x + 2/7 *Solve for y. (Note: +2/7 not -2/7).

f^-1 = 1/7 x + 2/7 *f-inverse.

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

y = x

Answer 3

f'(x) = (x + 2) / 7