f(x) = (4 − x)^(1/2)
what is the inverse if x is less than or equal to 0?

Question

jim_thompson5910 · Answer

f(x) = (4 − x)^(1/2) 


f(x) = sqrt(4 − x) 


y = sqrt(4 − x) 


x = sqrt(4 − y) 


x^2 = 4 - y 


x^2-4 = -y 


-x^2+4 = y


4-x^2 = y


y = 4-x^2 


Inverse is g(x) = 4-x^2  where x >= 0

anonymous · Answer

would the answer be any different if x

jim_thompson5910 · Answer

oh wait, yes it would, one sec

jim_thompson5910 · Answer

Inverse is g(x) = 4-x^2 where x >= 2

anonymous · Answer

so it just changes the way the graph looks?

anonymous · Answer

the domain

jim_thompson5910 · Answer

why x >= 2, because the range of f(x) is y >= 2

Remember that the domain and range swap when it comes to inverses

jim_thompson5910 · Answer

yes it changes the way it looks because different pieces are being drawn

anonymous · Answer

ok i understand, thanks again jim!!