(a) Define the term “range” of a real-valued function. (b) State the range of each of…

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

Problem

(a) Define the term “range” of a real-valued function. (b) State the range of each of the following standard functions defined on the set of all real numbers wherever the rule is meaningful: (i) Constant function f(x)=cf(x)=c where cc is a fixed real constant. (ii) Identity function f(x)=xf(x)=x. (iii) Modulus function f(x)=∣x∣f(x)=|x|. (iv) Signum function f(x)=sgn⁡(x)f(x)=\operatorname{sgn}(x). (v) Exponential function f(x)=axf(x)=a^{x} where a>1a>1. (vi) Logarithmic function f(x)=log⁡axf(x)=\log_{a}x where a>1a>1. (vii) Greatest integer function f(x)=⌊x⌋f(x)=\lfloor x\rfloor. Write each answer using set notation.

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