The function can be written as a composition

MATHEMATICS · Single correct · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

The function

h(x)=\sqrt{5-4x^{2}}

can be written as a composition

h(x)=p(q(x))

, where

p

and

q

are differentiable. Which of the following pairs

(p,q)

is valid? (a)

p(u)=5-u,\;q(x)=4x^{2}

(b)

p(u)=\sqrt{u},\;q(x)=5-4x^{2}

(c)

p(u)=\sqrt{5-u},\;q(x)=x^{2}

(d)

p(u)=5-4u^{2},\;q(x)=\sqrt{x}