Let $\mathrm{f}: \mathbf{R} \rightarrow \mathbf{R} ; \mathbf{f}(\mathbf{x})=\frac{x}{c}$, where $\mathbf{c}$ is a constant.
Find
(i) (cf) (x)
(ii) $\left(\mathrm{c}^{2} \mathrm{f}\right)(\mathrm{x})$
(iii) $\left(\frac{1}{c} f\right)(x)$
Given:
$\mathrm{f}(\mathrm{x})=\frac{x}{c}$
(i) To find:(cf) (x)
$(c f)(x)=c . f(x)$
$=c .\left(\frac{x}{c}\right)$
= x
Therefore,
$(c f)(x)=x$
(ii) To find: $\left(c^{2} f\right)(x)$
$\left(c^{2} f\right)(x)=c^{2} \cdot f(x)$
$=c .\left(\frac{x}{c}\right)$
= cx
Therefore,
$\left(c^{2} f\right)(x)=c x$
(iii) To find $\left(\frac{1}{c} f\right)(x)$
$\left(\frac{1}{c} f\right)=\frac{1}{c} \cdot f(x)$
$=\frac{1}{c}\left(\frac{x}{c}\right)$
Therefore,
$\left(\frac{1}{c} f\right)(x)=\frac{x}{c^{2}}$
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