What is the inverse of f(x)=3-0.5sqrt(2x+4) ?

The inverse of f(x)=3-0.5sqrt(2x+4) is 2(x^2-6x+8)

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inverse of f(x)=3-0.5sqrt(2x+4)

inverse

f (x) = 3 - 0.5 2 x + 4

2 (x^{2} - 6 x + 8)

Solution steps

y = 3 - 0.5 2 x + 4

Replace

x

with

y

x = 3 - 0.5 2 y + 4

Solve for

y, x = 3 - 0.5 2 y + 4

2 (x^{2} - 6 x + 8)

f (x) = (\frac{3}{4}) (10 x - 2)

f (x) = 15 x^{2} + 8 x + 4

\frac{3 x ^{2} - 18 x + 24}{x ^{2} - 4 x}

f (x) = \frac{x ^{2} - 4}{x ^{2} + 9}

f (x) = 6 - \frac{1}{2} x

What is the inverse of f(x)=3-0.5sqrt(2x+4) ?
The inverse of f(x)=3-0.5sqrt(2x+4) is 2(x^2-6x+8)