Suppose that The functions g and hare defined as follows. g(x)=4x^2-5 h(x)=2x-3 (a) Find ((g)/(h))(2) (b) Find all values that are NOT in the domain of (g)/(h) If there is more than one value, separate them with commas. (a) ((g)/(h))(2)= (b) Value(s) that are NOT in the domain of (g)/(h):square

## Step 1: Evaluate g(2) and h(2)<br />### We substitute $x=2$ into the expressions for $g(x)$ and $h(x)$.<br />$g(2) = 4(2^2) - 5 = 4(4) - 5 = 16 - 5 = 11$<br />$h(2) = 2(2) - 3 = 4 - 3 = 1$<br /><br />## Step 2: Calculate $(\frac{g}{h})(2)$<br />### We compute $(\frac{g}{h})(2)$ as $\frac{g(2)}{h(2)}$.<br />$(\frac{g}{h})(2) = \frac{g(2)}{h(2)} = \frac{11}{1} = 11$<br /><br />## Step 3: Find the values not in the domain of $\frac{g}{h}$<br />### The domain of $\frac{g}{h}$ is all real numbers except for values of $x$ where $h(x) = 0$. We solve $h(x) = 0$ for $x$.<br />$h(x) = 2x - 3 = 0$<br />$2x = 3$<br />$x = \frac{3}{2}$