What is the inverse of f(x)=((e^x+9)/2)^{1/2} ?

The inverse of f(x)=((e^x+9)/2)^{1/2} is ln(2x^2-9)

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inverse of f(x)=((e^x+9)/2)^{1/2}

inverse

f (x) = (\frac{e ^{x} + 9}{2})^{\frac{1}{2}}

ln (2 x^{2} - 9)

Solution steps

y = (\frac{e ^{x} + 9}{2})^{\frac{1}{2}}

Replace

x

with

y

x = (\frac{e ^{y} + 9}{2})^{\frac{1}{2}}

Solve for

y, x = (\frac{e ^{y} + 9}{2})^{\frac{1}{2}}

ln (2 x^{2} - 9)

tan (6 x)

(x - 1) (x - 7)

f (x) = 3 x - 1 g (x) = x^{3} + 1

f (x) = \frac{1}{12} (- x^{2} + 12 x - 32) + 0.25

f (x) = 2 (y - 3)^{2} + 5

What is the inverse of f(x)=((e^x+9)/2)^{1/2} ?
The inverse of f(x)=((e^x+9)/2)^{1/2} is ln(2x^2-9)