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Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsFunctions3 Marks
Question
Find $\text{f}+\text{g},\text{ f}-\text{g},\text{ cf}(\text{c}\in\text{ R},\text{c}\neq0),\text{ fg},\frac{1}{\text{f}}$ and $\frac{\text{f}}{\text{g}}$ in the following:
If $f(x) = x^3 + 1$ and $g(x) = x + 1$
✓

Answer

We have,
$f(x) = x^3 + 1$ and $g(x) = x + 1$
Now,
$f+g: R \rightarrow R$ is given by $(f+g)(x)=x^3+x+2$
$f-g: R \rightarrow R$ is given by $(f-g)(x)=x^3+1-(x+1)=x^3-x$.
$c f: R \rightarrow R$ is given by (cf) $(x)=c\left(x^3+1\right)$.
$(f g)(x): R \rightarrow R$ is given by $(f g)(x)=\left(x^3+1\right)(x+1)=x^4+x^3+x+1$
$\frac{1}{\text{f}}:\text{R}-\{-1\}\rightarrow\text{R}$ is given by $\Big(\frac{1}{\text{f}}\Big)(\text{x})=\frac{1}{\text{x}^3+1}$
$\frac{\text{f}}{\text{g}}:\text{R}-\{-1\}\rightarrow\text{R}$ is given by $\Big(\frac{\text{f}}{\text{g}}\Big)\text{(x)}=\frac{(\text{x}+1)(\text{x}^2-\text{x}+1)}{(\text{x}+1)}=\text{x}^2-\text{x}+1$

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