Let $$ f(x)=\frac{x+1}{x+8} $$ $$ f^{-1}(-4)=\square $$

Question

UpStudy AI · Accepted Answer

To find the value of $$ f^{-1}(-4) $$, we need to find the value of $$ x $$ for which $$ f(x) = -4 $$.

Given the function $$ f(x) = \frac{x+1}{x+8} $$, we set it equal to -4 and solve for $$ x $$:

$$
\frac{x+1}{x+8} = -4
$$

To solve for $$ x $$, we can cross-multiply:

$$
x + 1 = -4(x + 8)
$$

Now, distribute the -4 on the right side:

$$
x + 1 = -4x - 32
$$

Next, we want to get all the $$ x $$ terms on one side and the constants on the other side. We can do this by adding $$ 4x $$ to both sides and subtracting 1 from both sides:

$$
x + 4x = -32 - 1
$$

This simplifies to:

$$
5x = -33
$$

Now, divide both sides by 5 to solve for $$ x $$:

$$
x = \frac{-33}{5}
$$

So, $$ f^{-1}(-4) = \frac{-33}{5} $$.
$$ f^{-1}(-4) = \frac{-33}{5} $$.

Let \( f(x)=\frac{x+1}{x+8} \) \( f^{-1}(-4)=\square \)

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Algebra Questions