Question(b) $f(x)=-x+3$ $$\begin{array}{l} g(x)=x+3 \\ f(g(x))=\square \\ g(f(x))=\square \end{array}$$ $f$ and $g$ are inverses of each other $f$ and $g$ are not inverses of each other

Studdy Solution
Determine if $f$ and $g$ are inverses:
For $f$ and $g$ to be inverses, both $f(g(x)) = x$ and $g(f(x)) = x$ must hold true.
From STEP_1, we found $f(g(x)) = -x$, which is not equal to $x$.
From STEP_2, we found $g(f(x)) = -x + 6$, which is also not equal to $x$.
Since neither $f(g(x)) = x$ nor $g(f(x)) = x$, $f$ and $g$ are not inverses of each other.
The compositions are: $$f(g(x)) = -x$$ $$g(f(x)) = -x + 6$$
Conclusion: $f$ and $g$ are not inverses of each other.