(a) Define the terms domain, co–domain and range of a real-valued function. (b) State…

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

Problem

(a) Define the terms domain, co–domain and range of a real-valued function. (b) State the domain and the range of each of the following standard functions, writing your answers in set notation: (i) the identity function f1(x)=xf_1(x)=x; (ii) the constant function f2(x)=5f_2(x)=5; (iii) the modulus function f3(x)=∣x∣f_3(x)=|x|; (iv) the exponential function f4(x)=2xf_4(x)=2^{x}; (v) the logarithmic function f5(x)=log⁡3xf_5(x)=\log_{3}x; (vi) the greatest integer (floor) function f6(x)=⌊x⌋f_6(x)=\lfloor x\rfloor; (vii) the signum function f7(x)=sgn⁡(x)f_7(x)=\operatorname{sgn}(x). (c) Verify, with reference to the appropriate definitions, that the value 00 does not belong to the range of f4(x)=2xf_4(x)=2^{x}.

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