Chapter 5: Q. 119 (page 287)

If $f (x) = a^{x}$ , show that $f (A + B) = f (A) . f (B)$ .

Short Answer

Expert verified

To prove $f (A + B) = f (A) . f (B)$ , first find $f (A), f (B)$ and substitute the values in the expression of RHS and solve the expression to obtain LHS.

Step by step solution

Step 1. Given information.

Consider the given question,

$f (x) = a^{x}, f (A + B) = f (A) . f (B)$

Then,

$f (A) = a^{A} f (B) = a^{B}$

Take RHS,

$f (A) . f (B) = (a^{A}) . (a^{B})$

Step 2. Use laws of exponents.

Using laws of exponents, $x^{m} . x^{n} = x^{m + n}$ ,

$f (A) . f (B) = a^{A} . a^{B} f (A) . f (B) = a^{A + B} f (A) . f (B) = f (A + B)$

Therefore, $L H S = R H S$ .

Hence, proved.

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If $f (x) = a^{x}$ , show that $f (A + B) = f (A) . f (B)$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use laws of exponents.

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