Find a formula for the inverse of the given function. f(x) = 6x + 7 5x − 8

Answer 1

Mark asks an excellent question. I assume that there is a division symbol.

With inverse problems, you solve for x in terms of y. Then, you switch x and y in the formula.

y = (6x + 7)/(5x - 8)

Multiply both sides by 5x - 8.

Then y(5x - 8) = 6x + 7

5xy - 8y = 6x + 7

5xy - 6x = 8y + 7

x(5y - 6) = 8y + 7

x = (8y + 7)/(5y - 6)

Switching y and x,

y = (8x + 7)/(5x - 6), or

f^-1(x) = (8x + 7)/(5x - 6)

There is no inverse when x = 6/5. Note how this coincides with the horizontal asymptote at 6/5 in the original function. Also, note how the horizontal asymptote for the inverse, 8/5, corresponds to the vertical asymptote with the original function.