What is the inverse of f(x)=3-2tanh(x) ?

The inverse of f(x)=3-2tanh(x) is arctanh(-(x-3)/2)

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inverse of f(x)=3-2tanh(x)

inverse

f (x) = 3 - 2 tanh (x)

arctanh (- \frac{x - 3}{2})

Solution steps

Solve for

tanh (x), y = 3 - 2 tanh (x)

tanh (x) = - \frac{y - 3}{2}

tanh (a) = b \Rightarrow a = arctanh (b)

arctanh (- \frac{y - 3}{2})

Substitute

y = x

arctanh (- \frac{x - 3}{2})

What is the inverse of f(x)=3-2tanh(x) ?
The inverse of f(x)=3-2tanh(x) is arctanh(-(x-3)/2)