Question

If function f: R → R defined by f(x) = 7 – 2x, then f-1 is given by​

Answer 1

Answer:

Let x1,x2∈R

Letf(x1)=f(x2)

⇒2x1+3=2x2+3

⇒x1=x2

Hence, f is injective.

Let y ∈ codomain R

Lety=f(x)

⇒y=2x+3

⇒x=y−32∈ domain R

Hence, f is onto (surjective).

∴f−1 exists.

∴f−1(x)=x−32,x∈R

Step-by-step explanation:

follow me if worked

Answer 2

Answer:

$f-1(x)=\frac{7-x}{2}$

Step-by-step explanation:

Given: $f: R- > R$

$f(x)=7-2x$

Let $f(x)=y$

Thus,

$y=7-2x\\2x=7-y\\x=\frac{7-y}{2}$

Thus, we get

$f-1(x)=\frac{7-x}{2}$