Solve 1:f(x)=5x^2-4

$$1 : f ( x ) = 5 x ^ { 2 } - 4$$

Solve for f (complex solution)

$$f=-\frac{x}{4-5x^{2}}$$

$$x\neq 0\text{ and }x\neq -\frac{2\sqrt{5}}{5}\text{ and }x\neq \frac{2\sqrt{5}}{5}$$

Steps for Solving Linear Equation

Variable f cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by f.

$$1x=5x^{2}f+f\left(-4\right)$$

Swap sides so that all variable terms are on the left hand side.

$$5x^{2}f+f\left(-4\right)=1x$$

Reorder the terms.

$$5fx^{2}-4f=x$$

Combine all terms containing f.

$$\left(5x^{2}-4\right)f=x$$

Divide both sides by 5x^{2}-4.

$$\frac{\left(5x^{2}-4\right)f}{5x^{2}-4}=\frac{x}{5x^{2}-4}$$

Dividing by 5x^{2}-4 undoes the multiplication by 5x^{2}-4.

$$f=\frac{x}{5x^{2}-4}$$

Variable f cannot be equal to 0.

$$f=\frac{x}{5x^{2}-4}\text{, }f\neq 0$$

Solve for f

$$f=-\frac{x}{4-5x^{2}}$$

$$x\neq 0\text{ and }|x|\neq \frac{2\sqrt{5}}{5}$$

Steps for Solving Linear Equation

Variable f cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by f.

$$1x=5x^{2}f+f\left(-4\right)$$

Swap sides so that all variable terms are on the left hand side.

$$5x^{2}f+f\left(-4\right)=1x$$

Reorder the terms.

$$5fx^{2}-4f=x$$

Combine all terms containing f.

$$\left(5x^{2}-4\right)f=x$$

Divide both sides by 5x^{2}-4.

$$\frac{\left(5x^{2}-4\right)f}{5x^{2}-4}=\frac{x}{5x^{2}-4}$$

Dividing by 5x^{2}-4 undoes the multiplication by 5x^{2}-4.

$$f=\frac{x}{5x^{2}-4}$$

Variable f cannot be equal to 0.

$$f=\frac{x}{5x^{2}-4}\text{, }f\neq 0$$

Solve for x

$$x=-\frac{\sqrt{80f^{2}+1}-1}{10f}$$

$$x=\frac{\sqrt{80f^{2}+1}+1}{10f}\text{, }f\neq 0$$