Question

hey! got a question with math, please help!

Part 1. Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are inverses.
f(x)=
x+a
b

g(x)=cx−d
Part 2. Show your work to prove that the inverse of f(x) is g(x).

Part 3. Show your work to evaluate g(f(x)).

Part 4. Graph your two functions on a coordinate plane. Include a table of values for each function. Include 5 values for each function. Graph the line y = x on the same graph.

Answer 1

f(x)= x+a

g(x)=cx−d

Your best bet is to go thru the actual steps of finding the inverse function of f(x), and then comparing the results to g(x).

Steps:

1. Replace f(x) with "y"
2. Interchange x and y

Please do these two things now; then we'll continue

Answer 2

hey sorry, i logged of for a minute, okay.

Answer 3

So y = x + a,
and interchange? sorry,

Answer 4

oh okay, for g(x)=cx−d, it would be
x = cy - d?

Answer 5

Let's concentrate of f(x) first.

In y = x + a, where you see x, substitute y; where you see y , substitute x.

Answer 6

oh, okay, so x = y + a?

Answer 7

Yes, very good. Now, please solve x = y + a for y.

Answer 8

(just subtract "a" from both sides of x = y + a)

Answer 9

okay, minus X from both sides and you get
Y = x - a

Answer 10

oh!!!! okay,,
i though you did x

Answer 11

so x - a = y?

Answer 12

yes, or y = x - a.

Now, replace y with the symbol for "inverse funtion of f(x)." It is:

Answer 13

\[f ^{-1}(x)\]

Answer 14

okay, so f−1(x) = x - a

Answer 15

oops, f^-1(x) = x - a