Question

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

Answer 1

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

Answer 2

would the answer be any different if x </=0 ?

Answer 3

oh wait, yes it would, one sec

Answer 4

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

Answer 5

so it just changes the way the graph looks?

Answer 6

the domain

Answer 7

why x >= 2, because the range of f(x) is y >= 2

Remember that the domain and range swap when it comes to inverses

Answer 8

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

Answer 9

ok i understand, thanks again jim!!