Engineering Mathematics Exam > Engineering Mathematics Videos > How to find two function inputs with the same output given graph (example) - Algebra, Mathematics
How to find two function inputs with the same output given graph (example) - Algebra, Mathematics Video Lecture - Engineering Mathematics
FAQs on How to find two function inputs with the same output given graph (example) - Algebra, Mathematics Video Lecture - Engineering Mathematics
| 1. How can I find two function inputs with the same output given a graph? |  |
Ans. To find two function inputs with the same output given a graph, you need to look for points on the graph where the y-coordinate (output) is the same for different x-coordinates (inputs). These points represent the desired inputs that produce the same output.
| 2. Is it always possible to find two function inputs with the same output from a graph? | |
Ans. No, it is not always possible to find two function inputs with the same output from a graph. Some functions may have a one-to-one correspondence between inputs and outputs, meaning each input produces a unique output. In such cases, you won't find any points on the graph where the output is repeated.
| 3. Can I find two function inputs with the same output by looking at the graph alone? | |
Ans. Yes, you can potentially find two function inputs with the same output by studying the graph. Look for any vertical lines that intersect the graph at more than one point. These points of intersection represent the desired inputs that produce the same output.
| 4. Are there any mathematical methods to find two function inputs with the same output other than graph analysis? | |
Ans. Yes, other than graph analysis, you can use algebraic methods to find two function inputs with the same output. Set the two expressions for the function equal to each other and solve for the variable. The resulting solution(s) will be the inputs that yield the same output.
| 5. How can I verify if two function inputs found from a graph indeed produce the same output? | |
Ans. To verify if two function inputs found from a graph produce the same output, substitute the inputs into the function and check if the resulting outputs are equal. If the outputs are the same, it confirms that the two inputs indeed yield the same output.
Text Transcript from Video
The graph of the function
f is shown below.
What is the input value
other than negative five
for which f of x is equal
to f of negative five?
So, we have our x axis,
we have our y axis.
And then in blue, they've
graphed y equals f of x.
So for example when
x is equal to one, f of x,
when y is going to be equal
to f of x --that's what this graph is--
f of x is equal to one.
When x is equal to seven,
f of seven, we see, is equal to five.
When x is equal to nine, we see
that f of nine is equal to six.
So what is the input value
other than negative five
for which f of x is equal to
f of negative five?
So, let's see.
If x is equal to negative five,
f of negative five is...
-- we move up here to the graph--
It is equal to four.
Cause this, once again, is the
graph y is equal to f of x.
So the y coordinate here,
this is what f of x, this is what
five of negative five is equal to.
So f of negative five is equal to four.
So where else does that happen?
So let's see.
Let's just move horizontally to the right.
That happens here as well.
So what input do we have to give?
What's the x coordinate here to get
y is equal to f of x or f of x is
equal to four right over here?
Well, we see the x
coordinate is also four.
So this tells us that f of four
is equal to four,
which is the same thing as
f of negative five.
So when x is four, the function
takes on the same value
as when x is negative five.
So x equals four. And we are done.
f is shown below.
What is the input value
other than negative five
for which f of x is equal
to f of negative five?
So, we have our x axis,
we have our y axis.
And then in blue, they've
graphed y equals f of x.
So for example when
x is equal to one, f of x,
when y is going to be equal
to f of x --that's what this graph is--
f of x is equal to one.
When x is equal to seven,
f of seven, we see, is equal to five.
When x is equal to nine, we see
that f of nine is equal to six.
So what is the input value
other than negative five
for which f of x is equal to
f of negative five?
So, let's see.
If x is equal to negative five,
f of negative five is...
-- we move up here to the graph--
It is equal to four.
Cause this, once again, is the
graph y is equal to f of x.
So the y coordinate here,
this is what f of x, this is what
five of negative five is equal to.
So f of negative five is equal to four.
So where else does that happen?
So let's see.
Let's just move horizontally to the right.
That happens here as well.
So what input do we have to give?
What's the x coordinate here to get
y is equal to f of x or f of x is
equal to four right over here?
Well, we see the x
coordinate is also four.
So this tells us that f of four
is equal to four,
which is the same thing as
f of negative five.
So when x is four, the function
takes on the same value
as when x is negative five.
So x equals four. And we are done.
About this Video
Sep 24, 2025
Last updated
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