The one-to-one functions g and h are defined as follows. g(x)=2x+13 h= (-5,4),(-1,1),(0,3),(3,-4) Find the following. g^-1(x)= square (g^-1cdot g)(-8)= square h^-1(3)= square

## Step 1: Find the inverse of $g(x)$<br />### To find the inverse of $g(x) = 2x + 13$, swap $x$ and $y$, then solve for $y$. Start with $y = 2x + 13$, rewrite as $x = 2y + 13$, and isolate $y$: <br />\[<br />x - 13 = 2y \quad \Rightarrow \quad y = \frac{x - 13}{2}.<br />\] <br />Thus, $g^{-1}(x) = \frac{x - 13}{2}$.<br /><br />## Step 2: Evaluate $(g^{-1} \cdot g)(-8)$<br />### Substitute $x = -8$ into $g(x)$ first:<br />\[<br />g(-8) = 2(-8) + 13 = -16 + 13 = -3.<br />\]<br />Then substitute $g(-8) = -3$ into $g^{-1}(x)$:<br />\[<br />g^{-1}(-3) = \frac{-3 - 13}{2} = \frac{-16}{2} = -8.<br />\]<br />Thus, $(g^{-1} \cdot g)(-8) = -8$.<br /><br />## Step 3: Find $h^{-1}(3)$<br />### The inverse of $h$ swaps the input and output values. From $h = \{ (-5,4), (-1,1), (0,3), (3,-4) \}$, the inverse is:<br />\[<br />h^{-1} = \{ (4,-5), (1,-1), (3,0), (-4,3) \}.<br />\]<br />Find $h^{-1}(3)$ by locating where $3$ is the input in $h^{-1}$:<br />\[<br />h^{-1}(3) = 0.<br />\]