If f(x) = mx +c and m ≠ 0, find the equation of the corresponding function g(x). Explain why we need the restriction ≠0 in this question. State why a function g(x) does or does not exist in the case m = 0.
please explain every step and in detail.
thank you very much!

Question

If f(x) = mx +c and m ≠ 0, find the equation of the corresponding function g(x). Explain why we need the restriction ≠0 in this question. State why a function g(x) does or does not exist in the case m = 0.
please explain every step and in detail.
thank you very much!

unklerhaukus · Answer

how is g(x) supposed to be related to f(x) ?

anonymous · Answer

g(x) is the inverse i think, sorry not sure.

unklerhaukus · Answer

that would make sense..

unklerhaukus · Answer

If 
    f(x) = m*x+c
and
    g(x) = f^-1 (x)

then
      x =  m*g(x)+c.

Solve this for g(x)

anonymous · Answer

ok,so g(x)=(x-c)/m 
is that right?
how would i explain why we need the restriction ≠0 in this question. State why a function g(x) does or does not exist in the case m = 0.

anonymous · Answer

i dont understand that last bit

unklerhaukus · Answer

can you ever divide by zero?

anonymous · Answer

no

unklerhaukus · Answer

well, that is why m cannot be zero,

unklerhaukus · Answer

g(x) = (x-c)/m 

g(x)  is only defined when  (x-c)/m  is defined,

(x-c)/m  is not defined when  m = 0