Question

Task 1

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

@campbell_st

Answer 2

so is

\[f(x) = \frac{x + a}{b}\]

Answer 3

yes

Answer 4

ok so look at the inverse... swap x and y

\[x = \frac{y + a}{b}\]

can you make y the subject...?

Answer 5

no?

Answer 6

ok... multiply both sides by b

\[bx = y + a\]

now you should be able to make y the subject...

Answer 7

how?

Answer 8

subtract a from both sides...

Answer 9

\[a + bx = y\]

Answer 10

well its subtract..
y = bx - a

now compare it to the inverse you are given

y = cx - d

what can you say about b, c and a and d..?

Answer 11

they are both the same ?

Answer 12

@campbell_st

Answer 13

So, when you do the inverse, it like the same?

Answer 14

it requires you to swap x and y and then make y the subject...

so all you need to do, from the way I see it... is to find the inverse of f(x)

compare it to g(x) and make the conclusion c = b and a = d

then pick numbers for a and b using the conclusion you will also have c and d

Answer 15

ohh ok