What is the inverse of f(x)=log_{10}(x-1)-2 ?

The inverse of f(x)=log_{10}(x-1)-2 is 10^{x+2}+1

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inverse of f(x)=log_{10}(x-1)-2

inverse

f (x) = lo g_{10} (x - 1) - 2

1 0^{x + 2} + 1

Solution steps

y = lo g_{10} (x - 1) - 2

Replace

x

with

y

x = lo g_{10} (y - 1) - 2

Solve for

y, x = lo g_{10} (y - 1) - 2

1 0^{x + 2} + 1

f (x) = \frac{( 2 x + 5 )}{( x - 7 )}

f (x) = \frac{2 ( x - 1 )}{81}

f (x) = \frac{2}{3} x - 1 + 12

x + 3 - 5

f (x) = 5 x^{2} - 10 x + 7

What is the inverse of f(x)=log_{10}(x-1)-2 ?
The inverse of f(x)=log_{10}(x-1)-2 is 10^{x+2}+1