Answered

From health tips to tech hacks, find it all on IDNLearn.com. Find the answers you need quickly and accurately with help from our knowledgeable and experienced experts.

1) Find the inverse function of f(x)=1/2x+3
2)Use composition to verify that they are inverse relations?
3) f^ Domain : Range:
4) f^-1 Domain : Range:

Sagot :

Subediprashantidn
 y = 1/2x + 3
change x and y

x = 1/2y + 3
now find the value of y and that is inverse function 

x - 3 =1/2 y
y = 2x- 6
 
f-(x) = 2x - 6


for both domain : ( - ∞ , + ∞ )

range f (x) : ( - ∞ , + ∞ )  - { 0 }
range f-(x) :( -∞ , +∞)
To find the inverse function you need to change [tex]f(x)[/tex] (call it [tex]y[/tex]) and [tex]x[/tex], then solve for [tex]y[/tex]:

[tex]y = \frac{1}{2}x+3 \\ x = \frac{1}{2}y + 3 \\ x - 3 = \frac{1}{2}y \\ 2x-6 = y[/tex]

So now you have [tex]f^{-1}(x) = 2x-6[/tex].

Composition to prove inverse relation: [tex]f \circ f^{-1} (x) = x[/tex]:

[tex]f(f^{-1}(x)) = \frac{1}{2}(2x-6)+3 = x - 3 + 3 = x \square[/tex]

Domain and Range of both functions is Real numbers since they are both linear equations.
Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.