Need help on a question

[rawrness]

Find the inverse of the function
f(x) = 1- x/a, 0<a<1
Sketch f(x) and f^-1(x) (inverse) on the one set of axes
Find the point of intersection graphically and algebraically.

Please help and thanks in advance :3

[Zealous]

I'll do the easier part (finding the inverse) =p.. for the sketching I'm not sure since we have an idea of where a will be but we do not know for sure the value of a.



Swap x and y.

... simplify
... subtract 1 and divide by -1.



So the inverse



Now for sketching I'm not sure if you can even sketch it without knowing a.
In f(x) a is on the denominator, so if a is between 0 and 1, we could simply say a is 0.01 and the gradient will be -100 (very steep) or the line could almost look horizontal, so I'll let one of the fancy pants mathematicians take it from here.

[Daenerys Targaryen]

I'll do the easier part (finding the inverse) =p.. for the sketching I'm not sure since we have an idea of where a will be but we do not know for sure the value of a.



Swap x and y.

... simplify
... subtract 1 and divide by -1.



So the inverse

Sketching:




Because the intercepts of 'a' will be less than the 1 and above 0

For POI:
Let