Respuesta :

Answer:

see explanation

Step-by-step explanation:

(a)

let y = f(x), that is

5x + 3 = y

Rearrange making x the subject

Subtract 3 from both sides

5x = y - 3 ( divide both sides by 5 )

x = (y - 3) / 5, hence

[tex]f^{-1}[/tex](x) = (x - 3) / 5

(b)

[tex]f^{-1}[/tex](8) = (8 - 3) / 5 = 5/ 5 = 1

starlipika

part a:

f(x) = 5x + 3

set f(x) equal to y

y = 5x+3

swap x and y

x = 5y + 3

make y the subject

x - 3 = 5y

[tex]y = \frac{x - 3}{5} [/tex]

replace y with f^-1(x)

[tex] {f}^{ - 1} (x) = \frac{x - 3}{5} [/tex]

part b:

subsitute 8 as x into the inverse function

[tex] {f}^{ - 1} (x) = \frac{8 - 3}{5} [/tex]

= 5 ÷ 5

[tex] {f}^{ - 1} (8) = 1[/tex]

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