Questions: Given k(x)=-5x+6 and m(x)=x^2, (a) Find (k ∘ m)(x). (b) Find (m ∘ k)(x). (c) Is (k ∘ m)(x)=(m ∘ k)(x) ?

Transcript text: Given $k(x)=-5 x+6$ and $m(x)=x^{2}$, (a) Find $(k \circ m)(x)$. (b) Find $(m \circ k)(x)$. (c) Is $(k \circ m)(x)=(m \circ k)(x)$ ? Part: $0 / 3$ Part 1 of 3 (a) $(k \circ m)(x)=$ $\square$

Solution

Solution Steps

Step 1: Find the composition $(k \circ m)(x)$

To find $(k \circ m)(x)$, we substitute $m(x)$ into every occurrence of $x$ in $k(x)$. Thus, $(k \circ m)(x) = k(m(x)) = -119$.

Step 2: Find the composition $(m \circ k)(x)$

To find $(m \circ k)(x)$, we substitute $k(x)$ into every occurrence of $x$ in $m(x)$. Thus, $(m \circ k)(x) = m(k(x)) = 361$.

Step 3: Determine if the composition of functions is commutative

Since $(k \circ m)(x) \neq (m \circ k)(x)$ for some $x$, the composition of functions is not commutative.

Final Answer:

The composition of the given functions is not commutative.

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