Question

11, A function is defined by f(x) = 3x +4.

Answer 1

Answer:

see explanation

Step-by-step explanation:

(a)

Given f( x) = 3x + 4 then to find f(k) substitute x = k into f(x), that is

f(k) = 3k + 4

Now f(k) = k, thus

3k + 4 = k ( subtract 4 from both sides )

3k = k - 4 ( subtract k from both sides )

2k = - 4 ( divide both sides by 2 )

k = - 2

---------------------------------------------------------

(b)

let y = f(x) and rearrange making x the subject

y = 3x + 4 ( subtract 4 from both sides )

y - 4 = 3x ( divide both sides by 3 )

$\frac{y-4}{3}$ = x

Change y back into terms of x, thus

$f^{-1}$(x) = $\frac{x-4}{3}$