Let f - R - R - f x - x 2 and g - R - R - g x -2 x -1- Findi f - g x ii f - g x iii fg x iv f-gx

Here, dom (f) = R and dom (g) = R ∴dom (f)∩dom (g) = (R ∩ R)=R (i) (f+g):R → R is given by (f+g)(x)=f(x)+g(x)=x^2+(2x+1)=(x+1)^2 (ii) (f g):R → R is given by (f ...

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Byju's Answer

Standard XII

Mathematics

Limit

Let f : R → R...

Question

Let $f : R \to R : f (x) = x^{2}$ and $g : R \to R : g (x) = 2 x + 1$ . Find

(i) $(f + g) (x)$

(ii) $(f - g) (x)$

(iii) $(f g) (x)$

(iv) $(\frac{f}{g}) (x)$

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Solution

Here, $dom (f) = R$ and $dom (g) = R$

$∴ dom (f) \cap dom (g) = (R \cap R) = R$

(i) $(f + g) : R \to R$ is given by

$(f + g) (x) = f (x) + g (x) = x^{2} + (2 x + 1) = (x + 1)^{2}$

(ii) $(f - g) : R \to R$ is given by

$(f - g) (x) = f (x) - g (x) = x^{2} - (2 x + 1) = (x^{2} - 2 x - 1)$

(iii) $(f g) : R \to R$ is given by

$(f g) (x) = f (x) . g (x) = x^{2} . (2 x + 1) = (2 x^{3} + x^{2})$

(iv) $\frac{f}{g} (x) : R \to R$ is given by
${x : g (x) = 0} = {x : 2 x + 1 = 0} = {\frac{- 1}{2}}$

$∴ dom (\frac{f}{g}) = R \cap R - {\frac{- 1}{2}} = R - {\frac{- 1}{2}}$

The function $\frac{f}{g} : R - {\frac{- 1}{2}} \to R$ is given by

$(\frac{f}{g}) (x) = \frac{f (x)}{g (x)} = \frac{x^{2}}{2 x + 1}, x \neq \frac{- 1}{2}$

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Let f:R→R:f(x)=x2 and g:R→R:g(x)=2x+1. Find (i) (f+g)(x) (ii) (f−g)(x) (iii) (fg)(x) (iv) (fg)(x)

Let $f : R \to R : f (x) = x^{2}$ and $g : R \to R : g (x) = 2 x + 1$ . Find

(i) $(f + g) (x)$

(ii) $(f - g) (x)$

(iii) $(f g) (x)$

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