Question

Let f(x) = 2x − 6. Solve f−1(x) when x = 2.

Answer 1

To find the inverse of ƒ(x) = 2x - 6, then let ƒ(x) be y
y = 2x - 6
=> Make x the subject of formula by adding 6 to both sides and then dividing by 2, which you'll have
(y + 6)/2 = x
=> Switch the x & y variables to get the inverse of y, then
(x + 6)/2 = y
=> Remember that ƒ(x) is y, so also the inverse of y is ƒ-1(x), then
ƒ-1(x) = (x + 6)/2, where x = 2, you'll have
ƒ-1(2) = (2 + 6)/2
ƒ-1(2) = 8/2
ƒ-1(2) = 4

Answer 2

If f(x) = 2x − 6 , therefore when x = 2 → f⁻¹(x) = 4

Further explanation

Function is a relation which each member of the domain is mapped onto exactly one member of the codomain.

There are many types of functions in mathematics such as :

• Linear Function → f(x) = ax + b

• Quadratic Function → f(x) = ax² + bx + c
• Trigonometric Function → f(x) = sin x or f(x) = cos x or f(x) = tan x
• Logarithmic function → f(x) = ln x
• Polynomial function → f(x) = axⁿ + bxⁿ⁻¹ + ...

If function f : x → y , therefore inverse function f⁻¹ : y → x

Let us now tackle the problem!

$f(x) = 2x - 6$

$y = 2x - 6$

$y + 6 = 2x$

$x = \frac{y + 6}{2}$

$f^{-1}(x) = \frac{x + 6}{2}$

When x = 2 :

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

$f^{-1}(2) = \frac{8}{2}$

$\large {\boxed {f^{-1}(2) = 4} }$

Learn more

• Inverse of Function : https://brainly.com/question/9289171
• Rate of Change : https://brainly.com/question/11919986
• Graph of Function : https://brainly.com/question/7829758

Answer details

Grade: High School

Subject: Mathematics

Chapter: Function

Keywords: Function , Trigonometric , Linear , Quadratic , Inverse