Questions: Find the inverse function (on the given interval, if specified) and graph both f and f^-1 on the same set of axes. Check by looking for the required symmetry in the graphs. f(x) = √(x-4) for x ≥ 4 Find the inverse function. f^-1(x) = for x ≥

Find the inverse function (on the given interval, if specified) and graph both f and f^-1 on the same set of axes. Check by looking for the required symmetry in the graphs.

f(x) = √(x-4) for x ≥ 4

Find the inverse function.

f^-1(x) = for x ≥

Transcript text: Find the inverse function (on the given interval, if specified) and graph both $f$ and $f^{-1}$ on the same set of axes. Check by looking for the required symmetry in the graphs. \[ f(x)=\sqrt{x-4} \text { for } x \geq 4 \] Find the inverse function. \[ f^{-1}(x)=\square \text { for } x \geq \square \]

Solution

Solution Steps

Step 1: Find the Inverse Function

To find the inverse function of $f(x) = \sqrt{x - 4}$, we solve for $x$ in terms of $y$, resulting in $f^{-1}(x) = \dfrac{x^2 + 4}{1}$.

Step 2: Specify the Domain of the Inverse

The domain of $f^{-1}$ is the range of $f$, which starts from $c = 4$ and extends to infinity or negative infinity, depending on the direction of the domain specified.

Step 3: Graphing

The graph shows both $f(x)$ and its inverse $f^{{-1}}(x)$, along with the line $y = x$ for symmetry check.

Step 4: Check for Symmetry

By observing the graph, we can confirm that $f(x)$ and $f^{{-1}}(x)$ are symmetric about the line $y = x$, verifying the correctness of the inverse function.