Question

Math

Posted 3 months ago

```
Functions $h$ and $f$ are graphed.
Find $\lim _{x \rightarrow-3} h(f(x))$.
Choose 1 answer:
(A) 4
(B) 1
(C) -3
(D) 2
(E) The limit doesn't exist
```

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Answer from Sia

Posted 3 months ago

Solution by Steps

step 2

Next, we need to find $h(f(-3))$. Since $f(-3) = 5$, we need to find $h(5)$. From the graph of $y = h(x)$, we see that $h(5) = 2$

step 3

Therefore, $\lim_{x \to -3} h(f(x)) = h(f(-3)) = h(5) = 2$

D

Key Concept

Composite Function Limit

Explanation

To find the limit of a composite function $\lim_{x \to a} h(f(x))$, first find the limit of the inner function $f(x)$ as $x$ approaches $a$, and then find the value of the outer function $h$ at that limit.

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