Question

Let f, g: R → R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f + g, f – g and f/g.​

Answer 1

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$\Large\fbox{\color{purple}{QUESTION}}$

Let f, g: R → R be defined, respectively by f(x)

= x + 1, g(x) = 2x – 3. Find f + g, f – g and f/g.

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$\bf\Huge\red{\mid{\overline{\underline{ ANSWER }}}\mid }$

➡️Given, the functions f, g: R → R is defined as

➡️f(x) = x + 1, g(x) = 2x – 3

➡️Now,

➡️(f + g) (x) = f(x) + g(x) = (x + 1) + (2x – 3) = 3x – 2

➡️Thus, (f + g) (x) = 3x – 2

➡️(f – g) (x) = f(x) – g(x) = (x + 1) – (2x – 3) = x + 1 – 2x + 3 = – x + 4

➡️Thus, (f – g) (x) = –x + 4

➡️f/g(x) = f(x)/g(x), g(x) ≠ 0, x ∈ R

➡️f/g(x) = x + 1/ 2x – 3, 2x – 3 ≠ 0

➡️Thus, f/g(x) = x + 1/ 2x – 3, x ≠ 3/2

$\Large\mathcal\green{FOLLOW \: ME}$

$\Large\mathcal\green{FOLLOW \: ME}$━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

$\huge\boxed{\underline{\underline{\green{\tt Solution}}}} </p><p>$

Here f, g: R → R be defined

•  f(x) = x + 1

• g(x) = 2x – 3

Now

$(f + g)(x)$

$= f(x) + g(x)$

$= (x + 1) + (2x - 3)$

$= 3x - 2$

AGAIN

$(f - g)(x)$

$= f(x) - g(x)$

$= (x + 1) - (2x - 3)$

$= x + 1 - 2x + 3$

$= - x + 4$

Now

$g(x) = 2x+3 \: vanishes \: at \: x = \frac{3}{2} </strong></p><p><strong>[tex]g(x) = 2x+3 \: vanishes \: at \: x = \frac{3}{2}$

$so \: the \: domain \: \frac{f}{g} \: is \: R - \{ \frac{3}{2} \}$

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

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

$= \frac{x + 1}{2x - 3}$

Therefore

f+g: R → R is defined by (f+g) (x) = 3x-2

f-g: R → R is defined by (f-g) (x) = - x+4

$\frac{f}{g} : R - \{ \frac{3}{2} \} → R \:  is \: defined \: by \: ( \frac{f}{g} ) (x) = \frac{x + 1}{2x - 3}$

$</p><p></p><p>\displaystyle\textcolor{red}{Please \: Mark \: it \: Brainliest}$