Question
Asked Dec 6, 2019
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Let f(x) = |x|, g(x) = x - 2, and h(x) =x°.
Write N(x) = x-4 as a composition of functions.
Choose the following composition that correctly defines N(x) = x- 4.
O A. goh
O B. fogoh
C. gog
D. hog
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Let f(x) = |x|, g(x) = x - 2, and h(x) =x°. Write N(x) = x-4 as a composition of functions. Choose the following composition that correctly defines N(x) = x- 4. O A. goh O B. fogoh C. gog D. hog

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Expert Answer

Step 1

The given functions are,

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f (x)=|x|,g(x)=x- 2 and h(x)=x To write N(x)= x - 4 as a composition of function, check the composition function in given options defines N(x).

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Step 2

Option (a...

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(g•h)(x)= g(h(x)) %3D = g(x') = x' - 2 %3D + N (x) Therefore, the option (a) is incorrect. Option (b) fogoh. (fogoh)(x)= f°g(h(x)) = f(8(x')) = f (x' - 2) = x* - 2| %3D + N (x) Therefore, the option (b) is incorrect.

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