What is the inverse of f(x)=(5(x-2)^2+1)/3 ?

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

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inverse of f(x)=(5(x-2)^2+1)/3

inverse

f (x) = \frac{5 ( x - 2 ) ^{2} + 1}{3}

\frac{3 x - 1}{5} + 2, - \frac{3 x - 1}{5} + 2

Solution steps

y = \frac{5 ( x - 2 ) ^{2} + 1}{3}

Replace

x

with

y

x = \frac{5 ( y - 2 ) ^{2} + 1}{3}

Solve for

y, x = \frac{5 ( y - 2 ) ^{2} + 1}{3}

\frac{3 x - 1}{5} + 2, - \frac{3 x - 1}{5} + 2

f (x) = e^{x + 5}

f (x) = - 2 - x^{2}, x \leq 0

f (x) = (x - 8)^{2} + 7

f (x) = 7 x^{2} + 4, x > 0

\frac{1}{2} x - 4

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