Multiple Choice 3 points h(n)=2n-2 g(n)=2n-5 Find (gcdot h)(n) 4n^2+7n-15 4n^2-14n+10 9n^2-3n-2 4n^2+14n+10

To solve for \((g \cdot h)(n)\), we need to compute the composition of the functions \(g(n)\) and \(h(n)\). This means substituting \(h(n)\) into \(g(n)\).<br /><br />### Step 1: Recall the given functions<br />- \(h(n) = 2n - 2\)<br />- \(g(n) = 2n - 5\)<br /><br />We are tasked with finding \((g \cdot h)(n) = g(h(n))\).<br /><br />---<br /><br />### Step 2: Substitute \(h(n)\) into \(g(n)\)<br />Substitute \(h(n) = 2n - 2\) into \(g(n) = 2n - 5\):<br />\[<br />g(h(n)) = g(2n - 2) = 2(2n - 2) - 5<br />\]<br /><br />---<br /><br />### Step 3: Simplify the expression<br />Expand and simplify:<br />\[<br />g(2n - 2) = 2(2n - 2) - 5<br />= 4n - 4 - 5<br />= 4n - 9<br />\]<br /><br />So, \(g(h(n)) = 4n - 9\).<br /><br />---<br /><br />### Step 4: Verify if this matches any of the provided options<br />The problem asks for \((g \cdot h)(n)\), but none of the provided answers match \(4n - 9\). It seems there may be a misunderstanding in the question or an error in the answer choices. Could you clarify or confirm the question?