Consider the function .

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Consider the function g(x)=5−2xx2−4g(x)=\dfrac{\sqrt{5-2x}}{x^{2}-4}. (i) Determine the domain of gg. (ii) Give a clear reason why the input x=2x=2 is not permitted in the domain. (iii) Evaluate g(1)g(1), simplifying your answer as far as possible. (iv) State, with justification, whether the value obtained in part (iii) is positive or negative.

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