consider the function.\n$f(x)=\frac{3}{4}x + 12$\nwhat is the y - intercept of $f^{-1}(x)$?\n-16\n-12\n$-\fra…

consider the function.\n$f(x)=\frac{3}{4}x + 12$\nwhat is the y - intercept of $f^{-1}(x)$?\n-16\n-12\n$-\frac{3}{4}$\n$\frac{4}{3}$

consider the function.\n$f(x)=\frac{3}{4}x + 12$\nwhat is the y - intercept of $f^{-1}(x)$?\n-16\n-12\n$-\frac{3}{4}$\n$\frac{4}{3}$

Answer

Explanation:

Step1: Find the inverse function

Let $y = f(x)=\frac{3}{4}x + 12$. Swap $x$ and $y$: $x=\frac{3}{4}y + 12$. Then solve for $y$: $x-12=\frac{3}{4}y$, so $y=\frac{4}{3}(x - 12)=\frac{4}{3}x-16$.

Step2: Find the y - intercept

The y - intercept of a function $y = g(x)$ is found by setting $x = 0$. For $y=\frac{4}{3}x-16$, when $x = 0$, $y=-16$.

Answer:

-16