Given that f(x)=x+1 and g(x)=1-x solve the inequality f(x)/g(x)>0

Expert Answers

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We have the functions f(x)=x+1 and g(x)=1-x.

Now f(x) / g(x) > 0

=> (x +1)/(1-x) >0

This is true if either both x +1 and 1-x are greater than 0 or both are less than 0.

Taking the first case

x+ 1> 0 and 1- x > 0

=> x > -1 and 1 > x

So x lies in (1 , -1)

The second case gives

x +1 < 0 and 1 - x < 0

=> x < -1 and -x < -1

=> x< -1 and x > 1

This is not possible.

Therefore x lies in (-1 , 1)

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