find the inverse of each of the given functions.\n$f(x)=4x - 12$\n$f^{-1}(x)=square x+square$\n$h(x)=\frac{2x…

Explanation:

Step1: Set $y = f(x)$

Let $y = 4x-12$.

Step2: Solve for $x$ in terms of $y$

Add 12 to both sides: $y + 12=4x$. Then divide both sides by 4, we get $x=\frac{y + 12}{4}=\frac{1}{4}y+3$.

Step3: Replace $y$ with $x$ to find the inverse

$f^{-1}(x)=\frac{1}{4}x + 3$.

For $h(x)=\frac{2x - 4}{3}$:

Step1: Set $y = h(x)$

Let $y=\frac{2x - 4}{3}$.

Step2: Solve for $x$ in terms of $y$

Multiply both sides by 3: $3y=2x - 4$. Then add 4 to both sides: $3y + 4=2x$. Divide both sides by 2, we have $x=\frac{3y + 4}{2}$.

Step3: Replace $y$ with $x$ to find the inverse

$h^{-1}(x)=\frac{3x + 4}{2}$.

Answer:

$f^{-1}(x)=\frac{1}{4}x + 3$, $h^{-1}(x)=\frac{3x + 4}{2}$