Suppose that function f- satisfies fx-y-fxfy for all x- y- and f1-3-If -i-1nfi-363- then n is equal to

F(x+y)=f(x)f(y) f(x)=a^x ⇒ f(1)=a=3 f(x)=3^x ∑_i=1^nf(i)=363 ⇒ 3+3^2+3^3+....+3^n=363 ⇒3(3^n 1)2=363⇒ n=5 nbsp; ...

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Standard XII

Mathematics

Properties of Determinants

Suppose that ...

Question

Suppose that function $f : R \to R$ satisfies $f (x + y) = f (x) f (y)$ for all $x, y \in R$ and $f (1) = 3$ .If $\sum_{i = 1}^{n} f (i) = 363$ , then $n$ is equal to

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5.000

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5.0

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5.00

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Solution

$f (x + y) = f (x) f (y)$
$f (x) = a^{x}$
$\Rightarrow f (1) = a = 3$
$f (x) = 3^{x}$
$\sum_{i = 1}^{n} f (i) = 363$
$\Rightarrow 3 + 3^{2} + 3^{3} + . . . . + 3^{n} = 363$
$\Rightarrow \frac{3 (3^{n} - 1)}{2} = 363 \Rightarrow n = 5$

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Suppose that function f:R→R satisfies f(x+y)=f(x)f(y) for all x,y∈R and f(1)=3.If ∑ni=1f(i)=363, then n is equal to

f(x+y)=f(x)f(y) f(x)=ax ⇒f(1)=a=3 f(x)=3x ∑ni=1f(i)=363 ⇒3+32+33+....+3n=363 ⇒3(3n−1)2=363⇒n=5

Suppose that function $f : R \to R$ satisfies $f (x + y) = f (x) f (y)$ for all $x, y \in R$ and $f (1) = 3$ .If $\sum_{i = 1}^{n} f (i) = 363$ , then $n$ is equal to

$f (x + y) = f (x) f (y)$
$f (x) = a^{x}$
$\Rightarrow f (1) = a = 3$
$f (x) = 3^{x}$
$\sum_{i = 1}^{n} f (i) = 363$
$\Rightarrow 3 + 3^{2} + 3^{3} + . . . . + 3^{n} = 363$
$\Rightarrow \frac{3 (3^{n} - 1)}{2} = 363 \Rightarrow n = 5$