Question

Let f(x) = 4x + 3 and g(x) = -2x + 5. Find (f0g)(5)

Answer 1

(fog)(x) = f( g(x) ) Remember, which ever function is closest to the (x) gets substituted into the other function.

Here, x is replaced with 5.
(fog)(5) = f( g(5) )

g(5) = ... ?

Answer 2

I got -27, which i don;t think is write.....I don't really remember how to do inverse functions.

Answer 3

g(5) = -2(5) + 5 = -10 + 5 = -5

(fog)(5) = f ( g(5) ) = f(-5) = 4(-5) + 3 = -20 + 3 = -17

Ans: -17

Answer 4

This has nothing to do with inverse functions.

This is a composition of functions problem.

Answer 5

nvm, i got -5, but i'm still not clear on compisition of functions

Answer 6

Composition of functions is a fancy type of substitution.

You know how to do things like, example:

g(x) = -2x + 5
g(0) = -2(0) + 5
g(5) = -2(5) + 5
g(A) = -2A + 5
g(A+2) = -2(A+2) + 5

Answer 7

Those types of things are very similar to composition of functions.

Answer 8

A composition of two functions like (f o g)(x) is when you substitute g(x) for every x in f(x):

For example: Let f(x) = 4x + 3 and g(x) = -2x + 5

(f o g)(x) = f( g(x) ) = f(-2x + 5) = 4(-2x+5) + 3 (notice that I replaced x in the f function with (-2x + 5)

Answer 9

what about things like f*g? would you just do (4x+3)(-2x+5)

Answer 10

and things with the exponent -1?

Answer 11

Mulitplication can be written as either \(\large (f \cdot g)(x) = f(x) \cdot g(x) \)
(Notice that the small solid dot is use instead of the open dot \((f \circ g)(x)\) used in composition.)
or \(\large (fg)(x)= f(x) \cdot g(x) \) (with the f and g right next to each other)

Answer 12

The exponent of -1 can mean either inverse of reciprocal, depending where it is placed.

\( \large f^{-1}(x)\) is the inverse of f(x)

\( \large \left(f(x)\right)^{-1} = \dfrac{1}{f(x)}\) is the reciprocal of f(x).

Answer 13

And yes using the two functions from above, (f*g)(x) = (4x+3)(-2x+5) = ...

Answer 14

how do you find the inverse of f(x)?

Answer 15

Probably the most common way is to replace f(x) with y, and then exchange x with y and vise versa. Then solve the resulting equation for y. Finally, replace y with f^-1(x).

f(x) = 4x + 3
y = 4x + 3 (replace f(x) with y)
x = 4y + 3 (exchange x's and y's)
x - 3 = 4y (start solving the equation of y by subtracting from both sides)
(x - 3)/4 = y (divide both sides by 4)

So f^-1(x) = (x-3)/4