11, A function is defined by f(x) = 3x +4.
(a) Given that f(k)=k, find k. (b) Find the inverse of f.

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jimrgrant1 jimrgrant1 · Answer 1 · 2019-08-11T09:56:55+02:00

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

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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 )

[tex]\frac{y-4}{3}[/tex] = x

Change y back into terms of x, thus

[tex]f^{-1}[/tex](x) = [tex]\frac{x-4}{3}[/tex]