Test of a horizontal line.Suppose f is a function.F does not have an inverse if any horizontal line crosses the graph of f more than once.F does have an inverse if no horizontal line crosses the graph of f more than once
How do you calculate f's inverse?
- Finding a Function's Inverse
- Replace f(x) with y first, then.
- Every x must be replaced with a y, and vice versa.
- Solve the y-part of the equation from step two.
- In place of y, write f1(x) f 1 (x).
- Check that (ff1)(x)=x (f f f 1) (x) = x and (f1f)(x)=x (f f 1 f) (x) = x are both true to validate your work
f= {(1,2),(2,3),(3,5),(4,7)}
Dom(gof)=dom(f)={1,3,4}.
(gof)(1)=g{f(1)}=g(2)=3,
(gof)(3)=g{f(3)}=g(5)=1
(gof)(4)=g{f(4)}=g(1)
∴gof={(1,3),(3,1),(4,3)}.
To learn more about inverse functions refer
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The sum of two consecutive odd integers is at most 123. find the pair with the greatest sum
two consecutive odd integers
2x+1,2x+3
The sum of two consecutive odd integers is at most 123
2x+1+2x+3≤123
Solve for x
2x+1+2x+3≤123
4x+4≤123
4x+4-4≤123-4
4x≤119
4/4x≤119/4
x≤119/4
x≤29.25
Substitute any numbers into x that are equal to 29 or less that are consecutive odd integers.
2x+1,2x+3
2 (29)+1,2 (29)+3
58+1,58+3
59,61
Check: 59+61=120
The pair of consecutive odd integers that have a sum of at most 123 are 59 and 61.
Answer: koh-rien
Step-by-step explanation:
Answer:
The parabolic equation does not intersect the linear equation.
Explanation:
Given equation's:
To solve , use substitution method by inserting 2nd equation into 1st
when substituted y = -2x
collect terms
simplify
Find discriminant:
As the discriminant is negative, it tell us that they both does not intersect each other.
