What is the inverse of f(x)=4sqrt((7-x)/x) ?

The inverse of f(x)=4sqrt((7-x)/x) is (112)/(16+x^2)

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inverse of f(x)=4sqrt((7-x)/x)

inverse

f (x) = 4 \frac{7 - x}{x}

\frac{112}{16 + x ^{2}}

Solution steps

y = 4 \frac{7 - x}{x}

Replace

x

with

y

x = 4 \frac{7 - y}{y}

Solve for

y, x = 4 \frac{7 - y}{y}

\frac{112}{16 + x ^{2}}

y - 4 = \frac{1}{6} (x - 6)

f (x) = \frac{( x - 6 ) ^{3}}{2}

f (x) = x^{2} + y^{2} = 25

f (x) = \frac{x}{5} - 8

- 2 x^{2} + 5 x - 8

What is the inverse of f(x)=4sqrt((7-x)/x) ?
The inverse of f(x)=4sqrt((7-x)/x) is (112)/(16+x^2)