1 2 Multiple Choice 1 point For functions f(x)=6x^2 and g(x)=x+5 find (gcirc f)(x) 6x^2+60x+150 6x+5x^2 6x^2+5 180 Clear my selection Multiple Choice 1 point If the point (8,-14) is reflected over both the x-axis and the y-axis, where will the new point (x',y') be located? (8,-14) (8,14) (-8,-14) (-8,14) Clear my selection

Let's go through each question step by step.<br /><br />### Question 1: Finding \((g \circ f)(x)\)<br /><br />Given:<br />\[ f(x) = 6x^2 \]<br />\[ g(x) = x + 5 \]<br /><br />We need to find \((g \circ f)(x)\), which means we need to find \(g(f(x))\).<br /><br />1. First, compute \(f(x)\):<br /> \[ f(x) = 6x^2 \]<br /><br />2. Next, substitute \(f(x)\) into \(g(x)\):<br /> \[ g(f(x)) = g(6x^2) \]<br /><br />3. Apply the function \(g\) to \(6x^2\):<br /> \[ g(6x^2) = 6x^2 + 5 \]<br /><br />So, \((g \circ f)(x) = 6x^2 + 5\).<br /><br />The correct answer is:<br />\[ 6x^2 + 5 \]<br /><br />### Question 2: Reflecting the Point \((8, -14)\)<br /><br />To reflect a point over both the x-axis and the y-axis, we need to:<br /><br />1. Reflect over the x-axis: This changes the sign of the y-coordinate.<br /> \[ (8, -14) \rightarrow (8, 14) \]<br /><br />2. Reflect over the y-axis: This changes the sign of the x-coordinate.<br /> \[ (8, 14) \rightarrow (-8, 14) \]<br /><br />So, the new point \((x', y')\) will be located at \((-8, 14)\).<br /><br />The correct answer is:<br />\[ (-8, 14) \]<br /><br />### Summary of Answers:<br />1. \((g \circ f)(x) = 6x^2 + 5\)<br />2. The new point \((x', y')\) is \((-8, 14)\)