What is the inverse of f(x)=5+3sqrt(x-1) ?

The inverse of f(x)=5+3sqrt(x-1) is (x^2-10x+25)/9+1

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inverse of f(x)=5+3sqrt(x-1)

inverse

f (x) = 5 + 3 x - 1

\frac{x ^{2} - 10 x + 25}{9} + 1

Solution steps

y = 5 + 3 x - 1

Replace

x

with

y

x = 5 + 3 y - 1

Solve for

y, x = 5 + 3 y - 1

\frac{x ^{2} - 10 x + 25}{9} + 1

2 x + 64

f (x) = x^{2} + 6 x + 5

f (x) = \frac{( 3 x - 1 )}{2 x + 1}

f (x) = - 5 ln (x) - 3

y = \frac{2 x + 1}{3}

What is the inverse of f(x)=5+3sqrt(x-1) ?
The inverse of f(x)=5+3sqrt(x-1) is (x^2-10x+25)/9+1