What is the inverse of f(x)=3+log_{2}(7x-10) ?

The inverse of f(x)=3+log_{2}(7x-10) is (2^{x-3}+10)/7

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inverse of f(x)=3+log_{2}(7x-10)

inverse

f (x) = 3 + lo g_{2} (7 x - 10)

\frac{2 ^{x - 3} + 10}{7}

Solution steps

y = 3 + lo g_{2} (7 x - 10)

Replace

x

with

y

x = 3 + lo g_{2} (7 y - 10)

Solve for

y, x = 3 + lo g_{2} (7 y - 10)

\frac{2 ^{x - 3} + 10}{7}

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

2 - x

f (x) = \frac{3 x + 6}{x}

y = - 2 x - 3

f (x) = \frac{1}{x} - 5

What is the inverse of f(x)=3+log_{2}(7x-10) ?
The inverse of f(x)=3+log_{2}(7x-10) is (2^{x-3}+10)/7