A composite function can be written as $w(u(x))$, where $u$ and $w$ are basic functions.

Is $f(x)=\frac{\sqrt{x}}{4 x-1}$ a composite function? If so, what are the "inner" and "outer" functions?

Choose 1 answer:
(A) $f$ is composite. The "inner" function is $4 x-1$ and the "outer" function is $\sqrt{x}$.
(B) $f$ is composite. The "inner" function is $\sqrt{x}$ and the "outer" function is $4 x-1$.
(c) $f$ is not a composite function.

Question

A composite function can be written as $w(u(x))$, where $u$ and $w$ are basic functions.

Is $f(x)=\frac{\sqrt{x}}{4 x-1}$ a composite function? If so, what are the "inner" and "outer" functions?

Choose 1 answer:
(A) $f$ is composite. The "inner" function is $4 x-1$ and the "outer" function is $\sqrt{x}$.
(B) $f$ is composite. The "inner" function is $\sqrt{x}$ and the "outer" function is $4 x-1$.
(c) $f$ is not a composite function.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine if $f(x) = \frac{\sqrt{x}}{4x-1}$ is a composite function, we need to identify if it can be written in the form $w(u(x))$, where $u(x)$ and $w(x)$ are basic functions. ‖ ‖ step 2 ⋮ Let's consider $u(x) = \sqrt{x}$ and $w(u) = \frac{u}{4x-1}$. ‖ ‖ step 3 ⋮ Substituting $u(x)$ into $w(u)$, we get $w(u(x)) = \frac{\sqrt{x}}{4x-1}$, which matches $f(x)$. ‖ ‖ step 4 ⋮ Therefore, $f(x)$ can be written as a composite function $w(u(x))$ with $u(x) = \sqrt{x}$ and $w(u) = \frac{u}{4x-1}$. ‖ ‖ step 5 ⋮ The "inner" function is $u(x) = \sqrt{x}$ and the "outer" function is $w(u) = \frac{u}{4x-1}$. ‖ ∻Answer∻ ⚹ (B) $f$ is composite. The "inner" function is $\sqrt{x}$ and the "outer" function is $4x-1$. ⚹ ∻Key Concept∻ ⚹Composite Function⚹ ∻Explanation∻ ⚹A composite function is formed when one function is applied to the result of another function. In this case, $f(x) = \frac{\sqrt{x}}{4x-1}$ can be expressed as $w(u(x))$ where $u(x) = \sqrt{x}$ and $w(u) = \frac{u}{4x-1}$.⚹◊What is the process for determining if a function is composite and identifying the inner and outer functions in a composite⍭ Generate me a similar question◊

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