Let f ( x ) = 14 − x Calculate f ^-1(x)=

Answer 1

Let f(x) = 14 − x Calculate f^-1(x) = ??

Detailed Solution:

To find any inverse function, follow the following four steps:

1) Replace f(x) by y

f(x) = 14 – x ==> y = 14 – x

2) Interchange x and y

y = 14 – x ==> x = 14 – y

3) Solve for y

x = 14 – y ==> y = 14 – x

4) Replace the new y by f^-1(x) which is the inverse function solution

y = 14 – x ==> f^-1(x) = 14 – x <== Final Solution

Now, Check for f(x) = 14 − x and f^-1(x) = 14 – x

1) (f o f^-1)(x) = x ==> f(f^-1(x)) = x ==> f(14 – x) = x ==> 14 – (14 − x) = x ==> 14 – 14 + x = x ==> x = x

2) (f^-1 o f)(x) = x ==> f^-1(f(x)) = x ==> f^-1(14 – x) = x ==> 14 – (14 − x) = x ==> 14 – 14 + x = x ==> x = x

Answer 2

to get the inverse function, f^-1(x), I turn f(x) into y [ y=14-x]. Now switch y to x and x to y.

[x=14-y]. Then solve for y ! Replace your new y with f^-1(x) and you are done I could give you the answer but I'll give you a hint to know if you're correct... if f(14) =0 then f^-1(0) should equal 14.