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Chapter 5: Q. 118 (page 287)

Iffx=ax, show thatfx+h-fxh=ax.ah-1hh鈮�0.

Short Answer

Expert verified

To prove fx+h-fxh=ax.ah-1h, first substitute the values of fx,fx+hand solve to get the expression at the RHS.

Step by step solution

01

Step 1. Given information.

Consider the given question,

fx=ax,fx+h-fxh=ax.ah-1hh鈮�0

Substitute fx=ax,fx+h=ax+hin the given expression,

Take the LHS,

fx+h-fxh=ax+h-axh

02

Step 2. Use laws of exponents.

Using laws of exponents,xa.b=xa+xb,

=ax.ah-axh=ax.ah-1h

Therefore, LHS=RHS.

Hence, proved.

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