Given , and , which of the following represents…

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

Problem

Given f(x)=1x−2f(x)=\dfrac{1}{x-2}, g(x)=∣x∣g(x)=|x| and h(x)=x2−4x+3h(x)=x^{2}-4x+3, which of the following represents (f∘g∘h)(x)(f\circ g\circ h)(x)? (a) 1 ∣x2−4x+3∣+2 \displaystyle \frac{1}{\,|x^{2}-4x+3|+2\,} (b) 1x2−4x+1\displaystyle \frac{1}{x^{2}-4x+1} (c) 1 ∣x2−4x+3∣−2 \displaystyle \frac{1}{\,|x^{2}-4x+3|-2\,} (d) 1 ∣x2−4x+3−2∣ \displaystyle \frac{1}{\,|x^{2}-4x+3-2|\,}

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