If $$ h(x)=5+x $$ and $$ k(x)=\frac{1}{x} $$, which expression is equivalent to $$ (k \circ h)(x) $$ ? $$ \begin{array}{l}5+\left(\frac{1}{x}\right) \ 5+(5+x)\end{array} $$

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UpStudy AI · Accepted Answer

To find the expression equivalent to $$ (k \circ h)(x) $$, we need to evaluate the composition of the functions $$ k $$ and $$ h $$. The composition $$ (k \circ h)(x) $$ means we will substitute $$ h(x) $$ into $$ k(x) $$.

1. **Identify the functions:**
   - $$ h(x) = 5 + x $$
   - $$ k(x) = \frac{1}{x} $$

2. **Substitute $$ h(x) $$ into $$ k(x) $$:**
   $$
   (k \circ h)(x) = k(h(x)) = k(5 + x)
   $$

3. **Evaluate $$ k(5 + x) $$:**
   $$
   k(5 + x) = \frac{1}{5 + x}
   $$

Now, let's compare this result with the provided options:

- $$ 5 + \left(\frac{1}{x}\right) $$
- $$ 5 + (5 + x) $$

Neither of these options matches $$ \frac{1}{5 + x} $$. Therefore, the expression equivalent to $$ (k \circ h)(x) $$ is $$ \frac{1}{5 + x} $$, which is not listed among the options.
The expression equivalent to $$ (k \circ h)(x) $$ is $$ \frac{1}{5 + x} $$.

If and , which expression is equivalent to ?

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