Finite Math Examples

$f (x) = (x - 1) e^{3 - x}$

Step 1

Set $(x - 1) e^{3 - x}$ equal to $0$ .

$(x - 1) e^{3 - x} = 0$

Step 2

Solve for $x$ .

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Step 2.1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 1 = 0$

$e^{3 - x} = 0$

Step 2.2

Set $x - 1$ equal to $0$ and solve for $x$ .

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Step 2.2.1

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Step 2.2.2

Add $1$ to both sides of the equation.

$x = 1$

Step 2.3

Set $e^{3 - x}$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set $e^{3 - x}$ equal to $0$ .

$e^{3 - x} = 0$

Step 2.3.2

Solve $e^{3 - x} = 0$ for $x$ .

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Step 2.3.2.1

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (e^{3 - x}) = \ln (0)$

Step 2.3.2.2

The equation cannot be solved because $\ln (0)$ is undefined.

Undefined

Step 2.3.2.3

There is no solution for $e^{3 - x} = 0$

No solution

Step 2.4

The final solution is all the values that make $(x - 1) e^{3 - x} = 0$ true.

$x = 1$

Step 3