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Mathematics
Titan
27 January, 07:11
What is the inverse and domain of f (x) = x^2+4
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Konnor Roberson
27 January, 07:35
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The domain of the inverse of a function is the range of the original function
so find the range of f (x)
this is lowest to highest
we got the vertex is at (0,4)
and it goes to infinity
so range is from 4 to infinity
inverse
replace f (x) with y
switch x and y
solve for y
replace y with finverse
f (x) = x^2+4
y=x^2+4
x=y^2+4
x-4=y^2
y=√ (x-4)
f⁻¹ (x) = √ (x-4)
inverse is f⁻¹ (x) = √ (x-4)
the domain is x≥4
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Yaritza Calderon
27 January, 08:29
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To find the inverse let
y = x^2 + 4
x^2 = y - 4
x = sqrt (y - 4)
inverse f-1 (x) = sqrt (x - 4)
the domain of x^2 + 4 is all real x
the domain of f-1 (x) is x> = 4
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