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Chapter 4: Q. 79 (page 375)

Prove that if two functions F and G differ by a constant, then [F(x)]ab=[G(x)]ab.

Short Answer

Expert verified

Ans:

[G(x)]*=[F(x)+C]0k=(F(b)+C)-(F(a)+C)=F(b)-F(a)=[G(x)]4b

Step by step solution

01

Step 1. Given Information: 

Functions F and G differ by a constant

[F(x)]ab=[G(x)]ab
02

Step 2. Prove:

Now,itisclearthatG(x)-F(x)=C鈬�G(x)=F(x)+C.[G(x)]*=[F(x)+C]0k=(F(b)+C)-(F(a)+C)=F(b)-F(a)=[G(x)]4b鈭�henceproved[F(x)]ab=[G(x)]ab

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