Range of basic function

[e^x]

Full question: A linear function exists such that f(x+2) - f(x) = 6. Determine the value of f^-1(x+2)-f^1(x)
Where I went wrong: I assumed the answer would be f^-1(8)-f^-1(6), but that's incorrect.
To clarify: f^-1(x) means inverse

 

[Deleted member 4993]

Full question: A linear function exists such that f(x+2) - f(x) = 6. Determine the value of f^-1(x+2)-f^1(x)
Where I went wrong: I assumed the answer would be f^-1(8)-f^-1(6), but that's incorrect.
To clarify: f^-1(x) means inverse

A linear function \(\displaystyle \ \to \ \ \) f(x) = A*x +B

f^-1(x) = ?

f(x+2) = ?

f^-1(x+2) = ?

 

[Dr.Peterson]

Full question: A linear function exists such that f(x+2) - f(x) = 6. Determine the value of f^-1(x+2)-f^1(x)
Where I went wrong: I assumed the answer would be f^-1(8)-f^-1(6), but that's incorrect.
To clarify: f^-1(x) means inverse

One way to start is to observe the relationship between f(x+2) - f(x) = 6 and the slope of the linear function. From this, you can directly answer the question, with the same sort of thinking. What do you think the slope of the inverse function will be?

SK's approach should work if you don't have the insights that my way depends on, but will take a lot longer.