Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x
F(x)= x-7/x+3 and g(x)= -3x-7/x-1

Answer 1

Do you know the idea WHAT ARE inverse functions?

Answer 2

Definition : function g(x) is inverse to to function f(x) if for every value y= f(x) that f has computed , we can RETURN back to the source to x by plugging (substituting) this y into g: so\[g(y) = x\]

Answer 3

So the sequence of TWO CONSECUTIVE OPERATIONS (computations) will always restore the original source x\[x \rightarrow f(x)=y \rightarrow g(y) = x\]

Answer 4

so check first that\[g \left( \frac{ x-7 }{ x } - 3 \right) = x\] for ANY x

Answer 5

Just substitute the expression int the computation that g is doing