Question

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

(a) Given that f(k)=k, find k. (b) Find the inverse of f.​

Answer 1

see explanation

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

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(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 )

`(y-4)/(3)` = x

Change y back into terms of x, thus

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