Verify if is the inverse of . Show To verify the inverse, check if and . Set up the composite result function. Evaluate by substituting in the value of into . Cancel the common factor of and . Cancel the common factors. Cancel the common factor. Combine the opposite terms in . Set up the composite result function. Evaluate by substituting in the value of into . Apply the distributive property. Cancel the common factor of . Cancel the common factor. Combine the opposite terms in . Since and , then is the inverse of . Algebra ExamplesFind the Inverse f(x)=4x-8 Step 2 Interchange the variables. Step 3 Rewrite the equation as . Add to both sides of the equation. Divide each term in by and simplify. Cancel the common factor of . Cancel the common factor. Step 4 Replace with to show the final answer. Step 5 Verify if is the inverse of . To verify the inverse, check if and . Set up the composite result function. Evaluate by substituting in the value of into . Cancel the common factor of and . Cancel the common factors. Cancel the common factor. Combine the opposite terms in . Set up the composite result function. Evaluate by substituting in the value of into . Apply the distributive property. Cancel the common factor of . Cancel the common factor. Combine the opposite terms in . Since and , then is the inverse of . Explanation:For inverse function, the x and y interchanges and then make y the subject again of the equation. See the working out below: Now make #y# the subject of the equation: #x = 4y + 8# So the inverse function is: $\begingroup$ So I just got back from a Calculus test and I have some trouble figuring out one of the questions, it states: "Calculate the inverse of the function $y=\dfrac{2x+1}{3-4x}$." What first came into my mind was to eliminate the denominator somehow. But I quickly realized that it would be rather difficult science the numerator is also of degree one. I then got desperate and just tried to move the denominator and got this expression witch did not help me at all. $$y(3-4x) = 2x+1$$ After several more equally stupid moves I gave up. Even now with the help of Wolfram Alpha I can not figure out how to solve it. Can anyone explain?
Lorenzo B. 2,2322 gold badges10 silver badges25 bronze badges asked Feb 1, 2017 at 14:21
$\endgroup$ 1 $\begingroup$ Good start. You have: $$y(3-4x)=2x+1$$ You can expand this to obtain: $$3y-4xy=2x+1$$ And you can gather all the $x$ terms together: $$-4xy-2x=1-3y$$ $$4xy+2x=3y-1$$ Now, you can factor out the $x$ on the left hand side. Can you continue? If not, feel free to ask. answered Feb 1, 2017 at 14:30
projectilemotionprojectilemotion 15.1k6 gold badges30 silver badges52 bronze badges $\endgroup$ 1 $\begingroup$ $$y=\frac{2x+1}{3-4x}=-\frac{2x+1}{4x-3}=-\frac{1}{2}-\frac{5}{8x-6}$$ So $$y+\frac{1}{2}=-\frac{5}{8x-6} \iff \frac{2}{2y+1}=\frac{6-8x}{5}$$ So $$\frac{10}{2y+1}=6-8x \iff x=\frac{3y-1}{4y+2}$$ A simpler solution is possible using matrices, I believe. The answer is thus $$f^{-1}(x)=\frac{3x-1}{4x+2}$$ answered Feb 1, 2017 at 14:24
S.C.B.S.C.B. 22.7k3 gold badges34 silver badges58 bronze badges $\endgroup$ 3 $\begingroup$ After your first step: $y(3-4x) = 2x+1\quad | -2x$ From the first to second line, I also multiplied out on the left hand side. From the second to third line, I factored out x. This can of course be solved quicker, I tried to do it in steps that are easy to follow. answered Feb 1, 2017 at 14:26
ShinjaShinja 1,3257 silver badges8 bronze badges $\endgroup$ $\begingroup$ We have to express $y $ in terms of $x $. That is our ultimate goal. We thus get on rearranging, $$3y-4xy =2x+1 \Rightarrow 3y-1 =x (2+4y)$$ $$x = \frac {3y-1}{2+4y} $$ This is our inverse function. It can also be expressed as $f^{-1}(x) = \frac {3x-1}{2+4x} $. Hope it helps. answered Feb 1, 2017 at 14:27 $\endgroup$ $\begingroup$ $$y=\frac{2x+1}{3-4x}$$ Chase the denominator away. $$y(3-4x)=2x+1$$ Expand. $$3y-4xy=2x+1$$ Move all $x$ to the right-hand side. $$3y-1=2x+4xy$$ Factor. $$3y-1=(2+4y)x$$ Divide. $$\frac{3y-1}{2+4y}=x$$ answered Feb 1, 2017 at 14:34 $\endgroup$ How do we find the inverse of a function?How do you find the inverse of a function? To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.
How do you find the inverse of 4x?The equation which represents the inverse of the function f(x) = 4x is h(x) = 1/4 x.
How do you find the inverse of 8?The multiplicative inverse of 8 is 18 .
What is the inverse of 4?Answer and Explanation:
The multiplicative inverse of 4 is 1/4. (One-fourth is 1/4 in written form.)
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