The value of 'f' when 'g' is 16 is 24.
If 'f' is inversely proportional to square root of 'g', it can be expressed thus;
f [tex]\alpha[/tex] [tex]\frac{1}{\sqrt{g} }[/tex]
Then
f * [tex]\sqrt{g}[/tex] = constant
f₁*[tex]\sqrt{g}[/tex] ₁ = f₂ * [tex]\sqrt{g}[/tex]₂
If f₁ = 12 , [tex]\sqrt{g}[/tex]₁ = [tex]\sqrt{64}[/tex] = 8,
f₂ = ?, [tex]\sqrt{g}[/tex]₂= [tex]\sqrt{16}[/tex] = 4
Substitute into formula
12 * 8 = f₂ * 4
Make 'f₂' subject
f₂ = 96 ÷ 4
f₂ = 24
Therefore, the value of 'f' when 'g' is 16 is 24.
Learn more about indirect variations:
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