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Find the inverse function of $g(x)=-4x+1$.

So I replace $g(x)$ with $y$, then solve for $x$:

$$ 4x=1-y\\ x = \frac{1-y}4\\ y = \frac{1-x}4$$ The answer was $g(x)^{-1} =(-1/4)x + 1/4$.

Problem #12:

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$$ 1-x/4\neq (1-x)/4. $$ You forgot to divide everything by 4, as far as I can tell from your notation. – Ian Coley Mar 13 '14 at 1:43
That was a typo. It was suppose to be (1-x)/4. – igknighton Mar 13 '14 at 1:45
Your method and answer are essentially correct. I would skip the switcheroo between $x$ and $y$, though. If $y=g(x)$, then you should write the inverse function as $x=g^{-1}(y)$. Note also you should correct the placement of the "$-1$"--it should be written as $g^{-1}(y)$, not $g(y)^{-1}$. The latter signifies $\frac{1}{g(y)}$. Otherwise good! – MPW Mar 13 '14 at 2:00
up vote 1 down vote accepted

$$g(x)=-4x+1\\ \mbox{Let $g(x)=y$. Then, }-4x=y-1\\ x=(y-1)/(-4)\\ x=\dfrac{1-y}{4}\\ \boxed{g^{-1}(x)=\dfrac{1-x}{4}}$$ Or, simplifying, $$g^{-1}(x)=\dfrac{1-x}{4}\\ g^{-1}(x)=\dfrac{1}{4}-\dfrac{x}{4}=\dfrac{1}{4}-\dfrac{1}{4}x\\ \boxed{g^{-1}(x)=-\dfrac{1}{4}x+\dfrac{1}{4}}$$

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That's what I got for the answer, but this worksheet says otherwise.It's problem # 12.… – igknighton Mar 13 '14 at 1:46
@igknighton See my edited answer. – Sanath K. Devalapurkar Mar 13 '14 at 1:49
@igknighton Your answer's not wrong - it's a simplified form of the answer given at the link. – Sanath K. Devalapurkar Mar 13 '14 at 1:56

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