Solve Sketch the graph of f(1 - x) from graph of (x) = 1/x | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

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

Solve for f

$f=\frac{1}{\left(1-x\right)x^{2}}$
$x\neq 0\text{ and }x\neq 1$

Steps for Solving Linear Equation

Multiply both sides of the equation by $x$.

$$f\left(1-x\right)xx=1$$

Multiply $x$ and $x$ to get $x^{2}$.

$$f\left(1-x\right)x^{2}=1$$

Use the distributive property to multiply $f$ by $1-x$.

$$\left(f-fx\right)x^{2}=1$$

Use the distributive property to multiply $f-fx$ by $x^{2}$.

$$fx^{2}-fx^{3}=1$$

Combine all terms containing $f$.

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

Divide both sides by $-x^{3}+x^{2}$.

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

Dividing by $-x^{3}+x^{2}$ undoes the multiplication by $-x^{3}+x^{2}$.

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

Divide $1$ by $-x^{3}+x^{2}$.

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