How do you write the inverse function for $f (x) = \frac{1}{2} x + 4$ $f(x)=1/2x+4$ ?

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Answer 1 · 2016-11-18T05:32:00

The answer is $f^{- 1} (x) = 2 (x - 4)$ $f^(-1)(x)=2(x-4)$

Let $y = \frac{x}{2} + 4$ $y=x/2+4$

Then, $\frac{x}{2} = y - 4$ $x/2=y-4$

$y = 2 (y - 4)$ $y=2(y-4)$

So, $f^{- 1} (x) = 2 (x - 4)$ $f^(-1)(x)=2(x-4)$

Verification

$f (f^{- 1} (x)) = f (2 (x - 4)) = \frac{1}{2} \cdot 2 (x - 4) + 4 = x$ $f(f^(-1)(x))=f(2(x-4))=1/2*2(x-4)+4=x$

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