Find the x and y Intercepts f(x)=2- square root of x+1

$f (x) = 2 - \sqrt{x + 1}$

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = 2 - \sqrt{x + 1}$

Solve the equation.

Rewrite the equation as $2 - \sqrt{x + 1} = 0$ .

$2 - \sqrt{x + 1} = 0$

Subtract $2$ from both sides of the equation.

$- \sqrt{x + 1} = - 2$

To remove the radical on the left side of the equation, square both sides of the equation.

${(- \sqrt{x + 1})}^{2} = {(- 2)}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 1}$ as ${(x + 1)}^{\frac{1}{2}}$ .

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

Simplify the left side.

Simplify ${(- {(x + 1)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $- {(x + 1)}^{\frac{1}{2}}$ .

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

Raise $- 1$ to the power of $2$ .

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

Multiply ${({(x + 1)}^{\frac{1}{2}})}^{2}$ by $1$ .

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

Multiply the exponents in ${({(x + 1)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(x + 1)}^{\frac{1}{2} \cdot 2} = {(- 2)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x + 1)}^{\frac{1}{2} \cdot 2} = {(- 2)}^{2}$

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

Raise $- 2$ to the power of $2$ .

$x + 1 = 4$

Move all terms not containing $x$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$x = 4 - 1$

Subtract $1$ from $4$ .

$x = 3$

x-intercept(s) in point form.

x-intercept(s): $(3, 0)$

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = 2 - \sqrt{(0) + 1}$

Simplify $2 - \sqrt{(0) + 1}$ .

Simplify each term.

Add $0$ and $1$ .

$y = 2 - \sqrt{1}$

Any root of $1$ is $1$ .

$y = 2 - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$y = 2 - 1$

Subtract $1$ from $2$ .

$y = 1$

y-intercept(s) in point form.

y-intercept(s): $(0, 1)$

List the intersections.

x-intercept(s): $(3, 0)$

y-intercept(s): $(0, 1)$

Find the x and y Intercepts f(x)=2- square root of x+1

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