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

Q: 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

∻Solution by Steps∻ ‖ step 1 ⋮ To find $\lim_{x \to -3} h(f(x))$, we first need to determine $f(-3)$. From the graph of $y = f(x)$, we see that as $x$ approaches $-3$, $f(x)$ approaches $5$. Therefore, $f(-3) = 5$. ‖ ‖ 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.⚹◊What is the definition of the limit of a composite function as x approaches a certain value⍭ Generate me a similar question◊

Question

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

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find $\lim_{x o -3} h(f(x))$, we first need to determine $f(-3)$. From the graph of $y = f(x)$, we see that as $x$ approaches $-3$, $f(x)$ approaches $5$. Therefore, $f(-3) = 5$. ‖ ‖ 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, $\lim_{x o -3} h(f(x)) = h(f(-3)) = h(5) = 2$. ‖ ***D*** ∻Key Concept∻ ⚹Composite Function Limit⚹ ∻Explanation∻ ⚹To find the limit of a composite function $\lim_{x o a} h(f(x))$, 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.⚹◊What is the definition of the limit of a composite function as x approaches a certain value⍭ Generate me a similar question◊

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