Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 18, 2024

Find the composite function $(r \circ s)(x)$ where $r(x) = x + 1$ and $s(x) = 2x$ . Write the answer as a simplified polynomial.

STEP 1

Assumptions
1. The function $r(x)$ is defined as $r(x) = x + 1$ .
2. The function $s(x)$ is defined as $s(x) = 2x$ .
3. The composition of two functions $(r \circ s)(x)$ means applying $s$ first and then $r$ .

STEP 2

To find the composition $(r \circ s)(x)$ , we need to substitute $s(x)$ into $r(x)$ .
$(r \circ s)(x) = r(s(x))$

STEP 3

Substitute the expression for $s(x)$ into the function $r(x)$ .
$(r \circ s)(x) = r(2x)$

STEP 4

Now, apply the definition of $r(x)$ to the expression $r(2x)$ .
$(r \circ s)(x) = (2x) + 1$

STEP 5

Simplify the expression to get the polynomial in its simplest form.
$(r \circ s)(x) = 2x + 1$
The composition $(r \circ s)(x)$ is $2x + 1$ .

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