Let be defined by

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

Problem

Let f:R→[0,∞)f:\mathbb{R}\to[0,\infty) be defined by f(x)=∣x−3∣f(x)=|x-3|. To make ff invertible, its domain is restricted suitably. Which of the following choices gives a valid domain along with the correct expression for f−1(x)f^{-1}(x)? (a) Domain [3,∞)[3,\infty), f−1(x)=x−3f^{-1}(x)=x-3 (b) Domain [3,∞)[3,\infty), f−1(x)=3+xf^{-1}(x)=3+x (c) Domain (−∞,3](-\infty,3], f−1(x)=x−3f^{-1}(x)=x-3 (d) Domain [3,∞)[3,\infty), f−1(x)=∣x−3∣f^{-1}(x)=|x-3|

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