Mathematics

Mathematics

Problem

Let

F(x)=\ln|x|+x^{2}

and

G(x)=\ln|x|+x^{2}+7

. Which of the following statements is true? a) Both

F

and

G

are antiderivatives of

f(x)=\dfrac{1}{x}+2x

and

F(x)-G(x)=7

for all

x\ne0

. b) Both

F

and

G

are antiderivatives of

f(x)=\dfrac{1}{x}+2x

and

F(x)-G(x)=-7

for all

x\ne0

. c) Both

F

and

G

are derivatives of

f(x)=\dfrac{1}{x}+2x

. d) Only

G

is an antiderivative of

f(x)=\dfrac{1}{x}+2x

.

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