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Functions — MATHS STD 11 Science — Question

Gujarat 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 $g(x) = x + 1$
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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 $(f-g)(x)=x^3+1-(x+1)=x^3-x$. cf: $R \rightarrow R$ is given by $(c f)(x)=c\left(x^3+1\right) .(f g)(x): R \rightarrow R$ is given by $(f g)(x)=\left(x^3+1\right)(x+$ 1) $=x^4+x^3+x+1 \frac{1}{f}: R-\{-1\} \rightarrow R$ is given by $\left(\frac{1}{f}\right)(x)=\frac{1}{x^3+1} \frac{f}{g}: R-\{-1\} \rightarrow R$ 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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