Solve this

Question:

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) $\left(\frac{1}{c} f\right)(x)$

 

 

Solution:

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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