Composite Functions

[jsarwhite]

I need help trying to solve this problem for practice for my quiz: Use the following functions f(x) = x + 4 and g(x) = 2x - 5, to find the following:(g ^-1◦f ^-1)(x)
(f◦g) ^-1 (x)


I am completely confused with the negative exponents. Please help! Thank you in advance!

 

[Deleted member 4993]

I need help trying to solve this problem for practice for my quiz: Use the following functions f(x) = x + 4 and g(x) = 2x - 5, to find the following:(g ^-1◦f ^-1)(x)
(f◦g) ^-1 (x)


I am completely confused with the negative exponents. Please help! Thank you in advance!

What have you been taught about inverse of a function?

 

[pka]

I need help trying to solve this problem for practice for my quiz: Use the following functions f(x) = x + 4 and g(x) = 2x - 5, to find the following:(g ^-1◦f ^-1)(x)
(f◦g) ^-1 (x)

This is a plea for correct notation. Never, never write \(\displaystyle g\cdot f \) for composition. That notation actually means function multiplication. The correct notation is \(\displaystyle g\circ f \). In ordinary typing you can use gof.

I echo Mr. Khan, it would appear that you have not formally studied functions. Have you?
If \(\displaystyle (a,b)\in f \) then \(\displaystyle (b,a)\in f^{-1} \)
If \(\displaystyle (a,b)\in g\circ f \) then there is some \(\displaystyle c \) such that \(\displaystyle (a,c)\in f~\&~(c,b)\in g \).

Admittedly, that is advanced "stuff" for this level of algebra.

BUT you are given two lines.
It is very easy to find the inverse of a linear function: \(\displaystyle Ax+By+C=0 \) has inverse \(\displaystyle Bx+Ay+C=0 \)

 

[lookagain]

This is a plea for correct notation. Never, never write \(\displaystyle g\cdot f \) for composition. Yes, but the user did not type it that way.

I saw a central circle type symbol (for composition) without magnifying it. If you would use "View" at about 200%, it would likely confirm it.
But no one should have to magnify it to tell the difference between a composition symbol and a product symbol.

If the user had used the type/size of " \(\displaystyle g\circ f, \ \)" to begin with, it would not have fooled your eyes.

 

[stapel]

Use the functions f(x) = x + 4 and g(x) = 2x - 5 to find the following: (g ^-1 ◦ f ^-1)(x) and (f ◦ g) ^-1 (x)

I am completely confused with the negative exponents.

So you missed the classes (and maybe the chapter) on finding inverses of functions. Ouch! You can start your online self-study here.

If you missed the lessons (and maybe the chapter) on function composition, try here.

Once you have learned the basic terms and techniques, please attempt the exercise. If you get stuck, please reply showing all of your thoughts and efforts so far. Thank you!