What is the inverse of f(x)=2sqrt(x-1)+3 ?

The inverse of f(x)=2sqrt(x-1)+3 is (x^2+9)/4-(3x)/2+1

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inverse of f(x)=2sqrt(x-1)+3

inverse

f (x) = 2 x - 1 + 3

\frac{x ^{2} + 9}{4} - \frac{3 x}{2} + 1

Solution steps

y = 2 x - 1 + 3

Replace

x

with

y

x = 2 y - 1 + 3

Solve for

y, x = 2 y - 1 + 3

\frac{x ^{2} + 9}{4} - \frac{3 x}{2} + 1

11 x

y = 2 e^{x} - 1

10 x - 5 y = 25

f (x) = (7 - 10 x)^{\frac{9}{2}}

y = \frac{3 x - 6}{x - 2}

What is the inverse of f(x)=2sqrt(x-1)+3 ?
The inverse of f(x)=2sqrt(x-1)+3 is (x^2+9)/4-(3x)/2+1