F(x)= 5x+5

Question

Create a function that intersects between (5,5) and and that has f(x) and f inverse of x

Answer 1

5=5m+b passes through (5,5) where m=slope and b is y intercept. y=x (b=0 and m=1) fits. Also y=5x-20 (m=5, b=-20). f(x)=x is its own inverse.

Inverse of f(x) is found by putting y=f(x)=5x+5; 5x=y-5; x=y/5-1. Put g(y)=y/5-1, so g(y) is the inverse of f(x) and we can write f^-1(x)=x/5-1 as the inverse function. The inverse of f(x)=5x-20 is f^-1(x)=x/5+4 which passes through (5,5).

Answer 2

Given F(x)= 5x+5
passes from (x,y) = (5,5)
So the function is
y = mx+b
from above
m = 5
inverse interchange the x and y
5x = y-5
x = y/5-1
again
f^{-1}x=x/5-1
which passes from (5,5)

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