Consider the set of ordered pairs. Verify if it is one-to-one. If so, find its inverse.g={(1,32),(4,53),(7,94),(10,116)}g={\left\lbrace(1,\frac32),(4,\frac53),(7,\frac94),(10,\frac{11}{6})\right\rbrace}

g − 1 = { ( 3 2 , 1 ) , ( 5 3 , 4 ) , ( 9 4 , 7 ) , ( 11 6 , 10 ) } g^{-1}={\left\lbrace(\frac32,1),(\frac53,4),(\frac94,7),(\frac{11}{6},10)\right\rbrace}

Consider the set of ordered pairs. Verify if it is one-to-one. If so, find its inverse. g = { ( 1 , 3 2 ) , ( 4 , 5 3 ) , ( 7 , 9 4 ) , ( 10 , 11 6 ) } g={\left\lbrace(1,\frac32),(4,\frac53),(7,\frac94),(10,\frac{11}{6})\right\rbrace}

we're asked to consider the set of ordered pairs, verify if it is one to one, and if so, find its inverse. So here I have that G is equal to the set of ordered pairs one, three halves, four, five thirds, seven nine fourths, and ten eleven sixths. So before I find the inverse, I have to check that this even has an inverse by verifying that it's one to one. Remember when we're faced with a list of ordered pairs, what we're looking for is either repeated inputs or repeated outputs. Repeated inputs tells me that I'm not dealing with a function. And repeated outputs tells me that even if it is a function, it's not a one to one function. So that's what I'm looking for here. Now here I have no repeated inputs or outputs. I have one input and one output. It is a one to one function. So that means that it does have an inverse and I can proceed in finding it. So my in verse function of g here, that's g with a little negative one up top, this is going to be equal to the set of ordered pairs with reversed x and y values. So one and three one comma three halves, swapping those values. This is three halves, one. And then for my next ordered pair, four, five thirds, this is five thirds, four. Then for seven, nine fourths, swapping those values, nine fourths, seven. And finally, ten, eleven, sixths, swapping those values, I get eleven, six, 10. And then these are the ordered pairs that represent the inverse of g. Let us know if you have any questions, and I'll see you soon.

Consider the set of ordered pairs. Verify if it is one-to-one. If so, find its inverse. g = { ( 1 , 3 2 ) , ( 4 , 5 3 ) , ( 7 , 9 4 ) , ( 10 , 11 6 ) } g={\left\lbrace(1,\frac32),(4,\frac53),(7,\frac94),(10,\frac{11}{6})\right\rbrace}

g − 1 = { ( 3 2 , 1 ) , ( 5 3 , 4 ) , ( 9 4 , 7 ) , ( 11 6 , 10 ) } g^{-1}={\left\lbrace(\frac32,1),(\frac53,4),(\frac94,7),(\frac{11}{6},10)\right\rbrace}

g − 1 = { ( 2 3 , 1 ) , ( 3 5 , 1 4 ) , ( 4 9 , 1 7 ) , ( 6 11 , 1 10 ) } g^{-1}={\left\lbrace(\frac23,1),\left(\frac35,\frac14\right),(\frac49,\frac17),(\frac{6}{11},\frac{1}{10})\right\rbrace}

11. Inverse, Exponential, & Logarithmic Functions

Introduction to Inverse Functions

Intermediate Algebra

11. Inverse, Exponential, & Logarithmic Functions

Introduction to Inverse Functions

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Multiple Choice

Consider the set of ordered pairs. Verify if it is one-to-one. If so, find its inverse.
$g = {(1, \frac{3}{2}), (4, \frac{5}{3}), (7, \frac{9}{4}), (10, \frac{11}{6})}$

$g^{-1}={$\left\[\lbrace$(1,$\frac$23),$\left$($\frac$14,$\frac$35$\right$),($\frac$17,$\frac$49),($\frac{1}{10}$,$\frac{6}{11}$)$\right\]\rbrace$}$

$g^{- 1} = {(\frac{2}{3}, 1), (\frac{3}{5}, \frac{1}{4}), (\frac{4}{9}, \frac{1}{7}), (\frac{6}{11}, \frac{1}{10})}$

$g^{- 1} = {(\frac{3}{2}, 1), (\frac{5}{3}, 4), (\frac{9}{4}, 7), (\frac{11}{6}, 10)}$

The function is not one-to-one.

Verified step by step guidance

Identify the function for which you want to find the inverse. Let's denote the original function as $f(x)$.

Replace $f(x)$ with $y$ to make the equation easier to work with: write $y = f(x)$.

Swap the variables $x$ and $y$ in the equation. This means you rewrite the equation as $x = f(y)$, which is the key step in finding the inverse function.

Solve the new equation for $y$ in terms of $x$. This involves algebraic manipulation such as isolating $y$ on one side of the equation.

Once you have $y$ expressed as a function of $x$, rewrite it as $f^{-1}(x)$, which represents the inverse function.

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Struggling with Intermediate Algebra?

Consider the set of ordered pairs. Verify if it is one-to-one. If so, find its inverse.g={(1,32),(4,53),(7,94),(10,116)}g={\(\left\[\lbrace\)(1,\(\frac\)32),(4,\(\frac\)53),(7,\(\frac\)94),(10,\(\frac{11}{6}\))\(\right\]\rbrace\)}

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Consider the set of ordered pairs. Verify if it is one-to-one. If so, find its inverse.
$g = {(1, \frac{3}{2}), (4, \frac{5}{3}), (7, \frac{9}{4}), (10, \frac{11}{6})}$