Question

can someone help me with these??
1. given f(x)=11x-11, find the value below. (f*f^-1)*(-11)

2.let f(x)=3x+2 and g(x)=x^2-3x+2. perform the function operation and then find the domain. f(x)/g(x)

3.let f(x)=7-x and g(x)=2/x. perform the function operation and then find the domain of the result. (g-f)(x)

Answer 1

A. Hint:- (f*f^-1) of any function = x

Answer 2

so if we plug in x = -11 what do we get?

Answer 3

umm im not sure

Answer 4

@welshfella

Answer 5

You have at least two approaches to choose from to answer question a.

welshfella has shared with you an important property of functions and their inverses:
If we have both f(x) and the inverse function of x, as in

Answer 6

okay im following you i just honestly have no clue how to do these

Answer 7

perhaps a is too obvious...

Answer 8

?

Answer 9

More formally,

\[f(x) \rightarrow f ^{-1}(x)\]

Answer 10

function f(x) can be assumed to have an inverse in this particular problem.

What is the practical significance of using either f(x) or its inverse as the input to the other function? The end result is simply x.

\[f(f ^{-1}(x))=x\]

Answer 11

and \[f ^{-1}(f(x))=x\]

Answer 12

So, for example,
\[f(f ^{-1}(2))=2\]

Answer 13

Can you now evaluate\[f(f ^{-1}(-11))?\]

Answer 14

yeah i can im following you on what your saying

Answer 15

I'm so glad. Inverse functions are very useful in math, especially in calculus.

Now, knowing that\[f(f ^{-1}(x))=x,\]....
please evaluate \[f(f ^{-1}(-11)).\]

Answer 16

okay

Answer 17

I need your (numerical) response. Please also refer back to what welshfella has shared with you.