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For inequalities we contain a similar notation. Based on the complexity of the inequality the solution set might be a single number or it might be a range of numbers. If it is just one single number then we uses the same notation as we do for equations. If the solution set is a range of numbers, such as we looked at above is, we will use set builder notation. Following is the solution set for the inequality we looked at above.
{z | z ≥ -5}
It is read as : "The set of all z such that z is greater than or equal to -5".
Mostly inequalities that we will be looking at will have easy enough solution sets that we frequently just shorthand this as,
z ≥ -5
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Multiply following and write the answers in standard form. (a) 7 i ( -5 + 2 i ) (b) (1 - 5 i ) ( -9 + 2 i ) Solution (a) Thus all that we have to do is distribu
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f(x)+f(x+1/2) =1 f(x)=1-f(x+1/2) 0∫2f(x)dx=0∫21-f(x+1/2)dx 0∫2f(x)dx=2-0∫2f(x+1/2)dx take (x+1/2)=v dx=dv 0∫2f(v)dv=2-0∫2f(v)dv 2(0∫2f(v)dv)=2 0∫2f(v)dv=1 0∫2f(x)dx=1
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