What is the inverse of f(x)=4.5-2a^{0.5}(a-x)^{0.5} ?

The inverse of f(x)=4.5-2a^{0.5}(a-x)^{0.5} is -(x^2-9x+20.25-4a^2)/(4a)

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inverse of f(x)=4.5-2a^{0.5}(a-x)^{0.5}

inverse

f (x) = 4.5 - 2 a^{0.5} (a - x)^{0.5}

- \frac{x ^{2} - 9 x + 20.25 - 4 a ^{2}}{4 a}

Solution steps

y = 4.5 - 2 a^{0.5} (a - x)^{0.5}

Replace

x

with

y

x = 4.5 - 2 a^{0.5} (a - y)^{0.5}

Solve for

y, x = 4.5 - 2 a^{0.5} (a - y)^{0.5}

- \frac{x ^{2} - 9 x + 20.25 - 4 a ^{2}}{4 a}

What is the inverse of f(x)=4.5-2a^{0.5}(a-x)^{0.5} ?
The inverse of f(x)=4.5-2a^{0.5}(a-x)^{0.5} is -(x^2-9x+20.25-4a^2)/(4a)