f(x)=4x+3 g(x)=x^3-2x Find (fcdot g)(-3) -28 174 -62 189 Clear my selection

To find \((f \cdot g)(-3)\), we first need to determine the expression for \((f \cdot g)(x)\), which is the product of the functions \(f(x)\) and \(g(x)\).<br /><br />Given:<br />\[ f(x) = 4x + 3 \]<br />\[ g(x) = x^3 - 2x \]<br /><br />The product \((f \cdot g)(x)\) is:<br />\[ (f \cdot g)(x) = f(x) \cdot g(x) = (4x + 3)(x^3 - 2x) \]<br /><br />Now, substitute \(x = -3\) into this expression:<br /><br />1. Calculate \(f(-3)\):<br /> \[ f(-3) = 4(-3) + 3 = -12 + 3 = -9 \]<br /><br />2. Calculate \(g(-3)\):<br /> \[ g(-3) = (-3)^3 - 2(-3) = -27 + 6 = -21 \]<br /><br />3. Now calculate \((f \cdot g)(-3)\):<br /> \[ (f \cdot g)(-3) = f(-3) \cdot g(-3) = (-9) \cdot (-21) = 189 \]<br /><br />Therefore, the value of \((f \cdot g)(-3)\) is \(189\).