Composite Function Domain PDF

## Steps to Find the Domain of a Composite Function 1. Find the domain of the inside function 2. Find the domain of the composed function. 3. The final domain must include the restrictions of both (a) and (b). | | Function | | --- | -----------------------------------...

## Steps to Find the Domain of a Composite Function 1. Find the domain of the inside function 2. Find the domain of the composed function. 3. The final domain must include the restrictions of both (a) and (b). | | Function | | --- | ----------------------------------- | | f(x) | √x | | g(x) | ³√x | | h(x) | 1/x | | m(x) | x² | | n(x) | x + 5 | | p(x) | x² - 10x + 25 | ### Find the Composition and its Domain: a) _(f o n)_ (x) = f(n(x)) = f(x + 5) = √x + 5 D: {x | x ≥ -5} b) _(h o p)_ (x) = h(p(x)) = h(x² - 10x + 25) = 1/x² - 10x + 25 D: { x | x ≠ 5} c) _(f o m)_ (x) = f(m(x)) = f(x²) = √x² = |x| D: { x | x ∈ R} d) _(m o f)_ (x) = m(f(x)) = m(√x) = (√x)² = x D: { x | x ≥ 0} e) _(p o n)_ (x) = p(n(x)) = p(x + 5) = (x + 5)² - 10(x + 5) = x² + 10x + 25 - 10x - 50 + 25 = x² D: { x | x ∈ R } f) _(h o h)_ (x) = h(h(1/x)) = n(1/x) = 1/(1/x) = x D: { x | x ≠ 0} ### Circle the composition that produces each expression: | Expression | Composition | | ------------------------------ | -------------------------------------------- | | 1/x² | h(m(x)) | | x² - 10x² + 25 | p(m(x)) | | √x² + 5 | g(n(m(x))) | | 1/x | m(h(x)) | | (x² - 10x + 25)² | m(p(x)) | | n(g(m(x))) | | | m(g(n(x))) | | | g(n(m(x))) | |