What is the inverse of f(x)=3^{x-2}+7 ?

The inverse of f(x)=3^{x-2}+7 is (ln(x-7))/(ln(3))+2

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inverse of f(x)=3^{x-2}+7

inverse

f (x) = 3^{x - 2} + 7

\frac{ln ( x - 7 )}{ln ( 3 )} + 2

Solution steps

y = 3^{x - 2} + 7

Replace

x

with

y

x = 3^{y - 2} + 7

Solve for

y, x = 3^{y - 2} + 7

\frac{ln ( x - 7 )}{ln ( 3 )} + 2

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

\frac{4}{1 + x ^{2}}

(4 + 0.1 x) (100 - 5 x)

f (x) = (5 x - 3) + (- 8 x + 6) + (- 1 + 9 x)

\frac{1}{2} x + 5

What is the inverse of f(x)=3^{x-2}+7 ?
The inverse of f(x)=3^{x-2}+7 is (ln(x-7))/(ln(3))+2