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 over b

g(x)=cx−d

Question

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 over b

g(x)=cx−d

anonymous · Answer

I'm so confused. Please explain and not just give me the answer!

campbell_st · Answer

well basically a and d have the same value as does b and c

so pick some numbers

anonymous · Answer

a=2 and d=6 i guess

campbell_st · Answer

ok so 

$$f(x) = \frac{x + 2}{b}$$

then d is also 2

$$g(x) = cx - 2$$

campbell_st · Answer

so b and c have the same value

so b = 3 then c = 3

$$f(x) = \frac{x + 2}{3}~~~~g(x) = 3x - 2$$

anonymous · Answer

Oh okay.

anonymous · Answer

I also have to show work to prove that they are inverses. Would i just solve the equations?

anonymous · Answer

@campbell_st

campbell_st · Answer

ok... so look at the 1st equation 

$$y = \frac{c + a}{b}$$

so find th inverse swap x and y, then make y the subject

$$x = \frac{y + a}{b}$$

multiply both sides by b

$$bx = y + a$$

subtract a

$$bx - a = y~~~or~~~y = bx - a$$

this is the inverse of f(x) 

now compare it to g(x) = cx - d

o you can say b = c  and a = d

when you take the inverses