Sets, Relations & Functions Question - None

Question

Find the inverse of $f(x)=\dfrac{8^{2x}-8^{-2x}}{8^{2x}+8^{-2x}}$, $x\in(-1,1)$.

Accepted Answer

Let u=8^{2x}. y=(u^2-1)/(u^2+1). Solve: u^2=(1+y)/(1-y). So 4x=log_8((1+y)/(1-y))=(log_8e)ln((1+y)/(1-y)). f⁻^1(x)=(log_8e/4)ln((1+x)/(1-x)).

Trap: Remember log_8A=(log_8e)ln A.

Key Concept: (t-1/t)/(t+1/t) = (t^2-1)/(t^2+1) standard form

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