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Let f, g : R R be defined respectively by f(x) = x + 1, g(x)

Question

Let $f, g$ : $R \to R$ be defined respectively by $f (x) = x + 1, g (x) = 2 x - 3$ . Find $f + g, f - g$ and $\frac{f}{g}$

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Samuel Discussed

Let

f, g

R \to R

be defined respectively by

f (x) = x + 1, g (x) = 2 x - 3

. Find

f + g, f - g

and

\frac{f}{g}

7 mins ago

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7 mins ago

Text solutionVerified

f, g : R \to R

is defined as

f (x) = x + 1

g (x) = 2 x - 3

Now,

(f + g) (x) = f (x) + g (x) = (x + 1) + (2 x - 3) = 3 x - 2

∴ (f + g) (x) = 3 x - 2

Now,

(f - g) (x) = f (x) - g (x) = (x + 1) - (2 x - 3) = x + 1 - 2 x + 3 = - x + 4

∴ (f - g) (x) = - x + 4

(\frac{f}{g}) (x) = \frac{f ( x )}{g ( x )}, g (x) \neq = 0, x \in R

∴ (\frac{f}{g}) (x) = \frac{x + 1}{2 x - 3}, 2 x - 3 \neq = 0 or 2 x \neq = 3

∴ (\frac{f}{g}) (x) = \frac{x + 1}{2 x - 3}, x \neq = \frac{3}{2}

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Question Text	Let $f, g$ : $R \to R$ be defined respectively by $f (x) = x + 1, g (x) = 2 x - 3$ . Find $f + g, f - g$ and $\frac{f}{g}$
Answer Type	Text solution:1
Upvotes	150