Consider . Which of the following pairs is NOT a valid decomposition of as…

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Consider

h(x)=\ln\bigl(4x^{2}+1\bigr)

. Which of the following pairs

(f,\,g)

is NOT a valid decomposition of

h

g\circ f

? (a)

f(x)=x^{2},\; g(u)=\ln(4u+1)

(b)

f(x)=2x,\; g(u)=\ln(u^{2}+1)

(c)

f(x)=2x,\; g(u)=\ln(4u^{2}+1)

(d)

f(x)=4x^{2},\; g(u)=\ln(u+1)