Inverse Function Calculator

Calculate inverse functions with step-by-step solutions

Select Function Type

Linear Function: $f(x) = a \cdot x + b$

Coefficient a:

2

Coefficient b:

3

Quadratic Function: $f(x) = a \cdot x^2 + b \cdot x + c$

Coefficient a ($a \neq 0$):

1

Coefficient b:

-2

Coefficient c:

1

Domain Restriction:

For quadratic functions, we need to restrict the domain to make it one-to-one.

$x \geq -\frac{b}{2a}$

$x \leq -\frac{b}{2a}$

Vertex: $x = $1

Exponential Function: $f(x) = a \cdot e^{b \cdot x + c} + d$

Coefficient a ($a \neq 0$):

2

Coefficient b ($b \neq 0$):

1

Coefficient c:

0

Coefficient d:

0

Logarithmic Function: $f(x) = a \cdot \ln(b \cdot x + c) + d$

Coefficient a ($a \neq 0$):

2

Coefficient b ($b \neq 0$):

1

Coefficient c:

0

Coefficient d:

0

Original Function

$f(x) = 2x + 3$

Inverse Function

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

Domain: $x \in \mathbb{R}$

Step-by-Step Solution

Step 1: Replace $f(x)$ with $y$

$y = 2x + 3$

Step 2: Swap $x$ and $y$

$x = 2y + 3$

Step 3: Solve for $y$

$x - 3 = 2y$

$y = \frac{x - 3}{2}$

Step 4: Write the inverse function

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