Define the function H(x)= cases 2x+5,& -4 x<1

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Define the function H(x)={2x+5,−4≤x<1,x2,1≤x≤5.H(x)= \begin{cases} 2x+5,& -4\le x<1,\\ x^{2},& 1\le x\le5. \end{cases} (i) Write the domain of HH. (ii) Obtain the range of the linear branch 2x+52x+5 on −4≤x<1-4\le x<1. (iii) Obtain the range of the quadratic branch x2x^{2} on 1≤x≤51\le x\le5. (iv) Hence determine the complete range of HH. (v) State whether HH is continuous at x=1x=1, giving reason.

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