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Chapter 2: Q. 58 (page 168)

Show that iffis a function andz=x+hthen,

f(z)鈭�f(x)z鈭�x=f(x+h)鈭�f(x)h

Short Answer

Expert verified

Ans: The given expression f(z)鈭�f(x)z鈭�x=f(x+h)鈭�f(x)h(It is true).

Step by step solution

01

Step 1. Given information.

given,

f(z)鈭�f(x)z鈭�x=f(x+h)鈭�f(x)h

02

Step 2. Let f(x) be a function and z=x+h.

Then,

z-x=h

And

f(z)=f(x+h)

The objective is to show that

f(z)鈭�f(x)z鈭�x=f(x+h)鈭�f(x)h

Replace z=x+hand z-x=hin f(z)鈭�f(x)z鈭�x

f(z)鈭�f(x)z鈭�x=f(x+h)鈭�f(x)h

Hence, if fis a function and z=x+h,then

f(z)鈭�f(x)z鈭�x=f(x+h)鈭�f(x)h

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