1. The problem involves analyzing two trigonometric functions $f(x)$ (solid line) and $g(x)$ (dashed line) graphed against $x$. 2. From the graph description: - At point $A$, $f(x)$ has value $m$. - At position $k$ on the $x$-axis, $f(k) = 0$ since it crosses the $x$-axis. - At $x = k$, $g(x)$ reaches a peak, so $g(k)$ is a maximum. 3. Let's analyze each option: - $f(x) = g(A)$: This is not meaningful as $g(A)$ is a value, not a function. - $g(m) = f(m) = k$: $m$ is a $y$-value, so $g(m)$ and $f(m)$ are not defined since functions take $x$ as input. - $f(k) + g(k) = 2m$: At $k$, $f(k) = 0$ and $g(k)$ is a peak (likely $m$ or near it). So sum is $0 + g(k)$, which may not equal $2m$. - $g(m) = f(k) = m$: $f(k) = 0$ from the graph, so this is false. 4. The only consistent statement is that at $k$, $f(k) = 0$ and $g(k)$ is a peak, which corresponds to $g(k) = m$ and $f(k) = 0$. 5. Therefore, the correct relation is $g(k) = m$ and $f(k) = 0$. Final answer: $g(k) = m$ and $f(k) = 0$.