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Many-One Function

Let fx=x2 and...

Question

Let $f (x) = x^{2}$ and $g (x) = 2 x + 1$ be two real functions.Find $(f + g) (x), (f - g) (x), (f g) (x), \frac{f}{g} (x)$ .

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Solution

Given: $f (x) = x^{2}$ and $g (x) = 2 x + 1$
Step 1:Addition of two functions
$(f + g) (x) = f (x) + g (x)$ $= x^{2} + (2 x + 1)$ $= x^{2} + 2 x + 1$

Step 2:Subtraction of two functions
$(f - g) (x) = f (x) - g (x)$
$= x^{2} - (2 x + 1)$
$= x^{2} - 2 x - 1$

Step 3: Multiplication of two functions
$(f g) (x) = f (x) . g (x)$
$= x^{2} (2 x + 1)$
$= 2 x^{3} + x^{2}$

Step 4:Division of two functions
$\frac{f}{g} (x) = \frac{f (x)}{g (x)} = \frac{x^{2}}{2 x + 1}$
As denominator cannot be zero $∴ \frac{f}{g} (x) = \frac{x^{2}}{2 x + 1}, x \neq \frac{- 1}{2}$

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Many-One Function

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