Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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: http://www.kutasoftware.com/FreeWorksheets/Alg2Worksheets/Function%20Inverses.pdf

share|improve this question
2  
$$ 1-x/4\neq (1-x)/4. $$ You forgot to divide everything by 4, as far as I can tell from your notation. –  Ian Coley Mar 13 at 1:43
    
That was a typo. It was suppose to be (1-x)/4. –  igknighton Mar 13 at 1:45
1  
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 at 2:00

1 Answer 1

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, $$g^{-1}(x)=\dfrac{1-x}{4}\\ g^{-1}(x)=\dfrac{1}{4}-\dfrac{x}{4}=\dfrac{1}{4}-\dfrac{1}{4}x\\ \boxed{g^{-1}(x)=-\dfrac{1}{4}x+\dfrac{1}{4}}$$

share|improve this answer
    
That's what I got for the answer, but this worksheet says otherwise.It's problem # 12. kutasoftware.com/FreeWorksheets/Alg2Worksheets/… –  igknighton Mar 13 at 1:46
    
@igknighton See my edited answer. –  Sanath Devalapurkar Mar 13 at 1:49
    
@igknighton Your answer's not wrong - it's a simplified form of the answer given at the link. –  Sanath Devalapurkar Mar 13 at 1:56

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.