Question

Inverse functions and tangent lines. I'm not sure how to do this, I think there may not be enough info.

Answer 1

Recall that the graph of the inverse is the graph of the original function reflected about y=x.

Answer 2

we can get the graph of the inverse function and its tangent by simply reflecting in
y = x
if the tangent to f at P is y = 3x + 4

we can reflect and say that the tangent to inverse f at P is x = 3y + 4

Answer 3

oh, so just solve for y?

Answer 4

ya

Answer 5

y = (x- 4)/3

Answer 6

Find the inverse of the tangent line, it will be tangent to the inverse function. So....\[g(x)=y=3x+4\implies g^{-1}~implied~by~x=3y+4\implies y=\frac{x}{3}-\frac{4}{3} =g^{-1}(x)\]