Solve h^-1(5)=x^2+1

$$h ^ { - 1 } ( 5 ) = x ^ { 2 } + 1$$

Solve for h (complex solution)

$$h=\frac{5}{x^{2}+1}$$

$$x\neq i\text{ and }x\neq -i$$

Steps for Solving Linear Equation

Reorder the terms.

$$5\times \frac{1}{h}=x^{2}+1$$

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

$$5\times 1=hx^{2}+h$$

Multiply 5 and 1 to get 5.

$$5=hx^{2}+h$$

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

$$hx^{2}+h=5$$

Combine all terms containing h.

$$\left(x^{2}+1\right)h=5$$

Divide both sides by x^{2}+1.

$$\frac{\left(x^{2}+1\right)h}{x^{2}+1}=\frac{5}{x^{2}+1}$$

Dividing by x^{2}+1 undoes the multiplication by x^{2}+1.

$$h=\frac{5}{x^{2}+1}$$

Variable h cannot be equal to 0.

$$h=\frac{5}{x^{2}+1}\text{, }h\neq 0$$

Solve for h

$$h=\frac{5}{x^{2}+1}$$

Steps for Solving Linear Equation

Reorder the terms.

$$5\times \frac{1}{h}=x^{2}+1$$

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

$$5\times 1=hx^{2}+h$$

Multiply 5 and 1 to get 5.

$$5=hx^{2}+h$$

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

$$hx^{2}+h=5$$

Combine all terms containing h.

$$\left(x^{2}+1\right)h=5$$

Divide both sides by x^{2}+1.

$$\frac{\left(x^{2}+1\right)h}{x^{2}+1}=\frac{5}{x^{2}+1}$$

Dividing by x^{2}+1 undoes the multiplication by x^{2}+1.

$$h=\frac{5}{x^{2}+1}$$

Variable h cannot be equal to 0.

$$h=\frac{5}{x^{2}+1}\text{, }h\neq 0$$

Solve for x (complex solution)

$$x=-\sqrt{-1+\frac{5}{h}}$$

$$x=\sqrt{-1+\frac{5}{h}}\text{, }h\neq 0$$

Solve for x

$$x=\sqrt{-1+\frac{5}{h}}$$

$$x=-\sqrt{-1+\frac{5}{h}}\text{, }h>0\text{ and }h\leq 5$$