Question

section 4.1 - inverse functions
question 6 of 10 (1 point) | question attempt: 1 of unlimited
given
substitution
addition and subtraction properties
multiplication and division properties
since implies , the function is one - to - one.
part: 2 / 4
part 3 of 4
(b) write an equation for .

Explanation:

Step1: Let $y = f(x)$

Assume $y=2x - 1$ (since from the substitution step in the one - to - one proof, we can infer the function $f(x)=2x - 1$)

Step2: Swap $x$ and $y$

We get $x = 2y-1$

Step3: Solve for $y$

Add $1$ to both sides: $x + 1=2y$
Divide both sides by $2$: $y=\frac{x + 1}{2}$
So, $f^{-1}(x)=\frac{x + 1}{2}$

Answer:

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