What is the inverse of f(x)= 15/2 log_{3}(x-9)+4 ?

The inverse of f(x)= 15/2 log_{3}(x-9)+4 is 3^{(2x-8)/(15)}+9

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inverse of f(x)= 15/2 log_{3}(x-9)+4

inverse

f (x) = \frac{15}{2} lo g_{3} (x - 9) + 4

3^{\frac{2 x - 8}{15}} + 9

Solution steps

y = \frac{15}{2} lo g_{3} (x - 9) + 4

Replace

x

with

y

x = \frac{15}{2} lo g_{3} (y - 9) + 4

Solve for

y, x = \frac{15}{2} lo g_{3} (y - 9) + 4

3^{\frac{2 x - 8}{15}} + 9

y = 2 lo g_{3} (x)

f (x) = \frac{( x + 3 )}{( x + 5 )}

f (x) = \frac{5 + x ^{2}}{4}

f (x) = 48 x^{2} - 36

f (x) = 4 (9)^{2} + 5

What is the inverse of f(x)= 15/2 log_{3}(x-9)+4 ?
The inverse of f(x)= 15/2 log_{3}(x-9)+4 is 3^{(2x-8)/(15)}+9