Questions: If h(x)=5+x and k(x)=1/x, which expression is equivalent to (k ∘ h)(x) ? (5+x)/x 1/(5+x) 5+(1/x) 5+(5+x)

Transcript text: If $h(x)=5+x$ and $k(x)=\frac{1}{x}$, which expression is equivalent to $(k \circ h)(x)$ ? $\frac{(5+x)}{x}$ $\frac{1}{(5+x)}$ $5+\left(\frac{1}{x}\right)$ $5+(5+x)$

Solution

Solution Steps

Step 1: Understand the Composition of Functions

The problem asks for the expression equivalent to $ (k \circ h)(x) $. The notation $ (k \circ h)(x) $ represents the composition of the functions $ k(x) $ and $ h(x) $, which means we need to evaluate $ k(h(x)) $.

Step 2: Evaluate $ h(x) $

Given $ h(x) = 5 + x $, we substitute $ x $ into this function to get: \[ h(x) = 5 + x \]

Step 3: Substitute $ h(x) $ into $ k(x) $

Now, substitute $ h(x) = 5 + x $ into $ k(x) = \frac{1}{x} $: \[ k(h(x)) = k(5 + x) = \frac{1}{5 + x} \]