If point (a,b) lies on the graph y=f(x), the graph of f^-1 (x) must contain point:
Answers
Given:
Point (a,b) lies on the graph [tex]y=f(x)[/tex].
To find:
The point which is must be lies on the graph of [tex]y=f^{-1}(x)[/tex].
Solution:
According to the definition of an inverse function, if a function is defined as
[tex]f=\{(x,y):x\in R,y\in R\}[/tex]
then, its inverse is defined as
[tex]f^{-1}=\{(y,x):x\in R,y\in R\}[/tex]
It means, we have to interchange x and y-coordinate of the points which lies on the function f to get f⁻¹.
We have a point (a,b) lies on the graph [tex]y=f(x)[/tex]. So, (b,a) must be lies on the graph of [tex]y=f^{-1}(x)[/tex].
Therefore, the correct option is (1).
By the definition of inverse function,the point (a,b) lies on the graph [tex]\bold{y= f(x).}[/tex] So, (b,a) must be lies on the graph of [tex]\bold{y=f^{-1} (x)}[/tex].
Given:
Point (a,b) lies on the graph y= f(x).
Find:
The graph of [tex]\bold{y=f^{-1} (x)}[/tex] must contain that point.
As per the definition of inverse function, if two one-to-one functions f(x) and g(x). If (f∘g)(x)=x and (g∘f)(x)=x. Then, we say that f(x) and g(x) are inverses of each other.
[tex]\bold{f=\{ (x,y):x\epsilon R,y\epsilon R\}}[/tex]
Then, its inverse is defined as
[tex]\bold{f^{-1} =\{ (y,x):x\epsilon R,y\epsilon R\}}[/tex]
Therefore, we have to interchange x and y-coordinate of the points which lies on the function f to get f⁻¹.
Thus, the point (a,b) lies on the graph [tex]y= f(x).[/tex] So, (b,a) must be lies on the graph of [tex]y=f^{-1} (x)[/tex].
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Simplify the expression.
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Answers
1. -23(12c) -23 * -9 + 14c ( Apply the distributive property)
2. -276c -23 * -9 + 14c ( Multiply 12 by -23)
3. -276c + 207 + 14c
4. Add) -276c and 14c
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The simplification of the expression would be equal to -262c +207.
An equation is defined as an expression which shows the relationship between two or more numbers, variables, and a mathematical equation is a statement with two equal sides and an equal sign in between.
We are given the expression as;
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-23(12c) -23 * -9 + 14c
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-276c + 207 + 14c
Add -276c and 14c
-262c +207
The answer is -262c +207
Learn more about equations here;
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