What is the inverse of f(x)=2+5(3^{0.5x-2}) ?

The inverse of f(x)=2+5(3^{0.5x-2}) is (ln((9(x-2))/5))/(0.5ln(3))

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inverse of f(x)=2+5(3^{0.5x-2})

inverse

f (x) = 2 + 5 (3^{0.5 x - 2})

\frac{ln ( \frac{9 ( x - 2 )}{5} )}{0.5 ln ( 3 )}

Solution steps

y = 2 + 5 \cdot 3^{0.5 x - 2}

Replace

x

with

y

x = 2 + 5 \cdot 3^{0.5 y - 2}

Solve for

y, x = 2 + 5 3^{0.5 y - 2}

\frac{ln ( \frac{9 ( x - 2 )}{5} )}{0.5 ln ( 3 )}

f (x) = - 4 x + 16

f (x) = - x + 2 - 3

2 - 9 - (y + 2)^{2}

lo g_{10} (1)

What is the inverse of f(x)=2+5(3^{0.5x-2}) ?
The inverse of f(x)=2+5(3^{0.5x-2}) is (ln((9(x-2))/5))/(0.5ln(3))