Question

WILL FAN AND MEDAL
If the inverses of two functions are both functions, will the inverse of the sum or difference of the original functions also be a function? also provide 2 examples

Answer 1

@AloneS @mathmate @sweetburger

Answer 2

@Owlcoffee

Answer 3

suppose \(f(x)=2x+1\) and \(g(x)=2x-3\)
both have inverses because they are lines
what is \(f-g\)?

Answer 4

4?

Answer 5

@satellite73

Answer 6

Do you still need help with this one

Answer 7

yes

Answer 8

So lets take the example provided earlier, f(x)=2x+1, and g(x)=2x+3, \[f ^{-1}(x)=1/2x -1/2 \] and \[g ^{-1}(x)=1/2x-3/2 \], So yes the inverses are a function

Answer 9

i see

Answer 10

And now it is asking if the inverse of the sum of two functions would be a function, So we have f(x)-g(x) which would simply be f-g(x)=2x+1-2x+3, can you simplify that for me?

Answer 11

hold on

Answer 12

\[f-g=4\] in the example i gave, a number

Answer 13

a number (constant function) does not have an inverse

Answer 14

Sorry it should be f-g(x)=2x+1-2x-3

Answer 15

And that would be for the difference of the functions the sum of the functions would be f-g(x)=2x+1+2x+3

Answer 16

So what would that tell you about the sum of the functions and the difference of those given functions

Answer 17

that they are both functions?

Answer 18

No, that would tell you that the sum of the functions is but the difference of the functions is not for the example given