Question

Given that f(x)=2x+1, a) find f(2) b) find f -1(x) c) find f-1(7)

Answer 1

Answer:

see explanation

Step-by-step explanation:

Given

f(x) = 2x + 1

(a)

To evaluate f(2) substitute x = 2 into f(x), that is

f(2) = 2(2) + 1 = 4 + 1 = 5

(b)

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

y = 2x + 1 ( subtract 1 from both sides )

y - 1 = 2x ( divide both sides by 2 )

$\frac{y-1}{2}$ = x

change y back into terms of x and x = $f^{-1}$ (x) , thus

$f^{-1}$ (x ) = $\frac{x-1}{2}$

(c)

To evaluate the inverse function substitute x = 7, that is

$f^{-1}$ (7) = $\frac{7-1}{2}$ = $\frac{6}{2}$ = 3