Find the x and y Intercepts y=2x- square root of x^2+1

Problem

y=2*x−√(,x2+1)

Solution

1. Find the y-intercept by substituting x=0 into the equation.

y=2*(0)−√(,0+1)

y=0−√(,1)

y=−1

2. Set y to zero to begin finding the x-intercepts.

0=2*x−√(,x2+1)

3. Isolate the radical by moving it to the other side of the equation.

√(,x2+1)=2*x

4. Square both sides to eliminate the square root, noting that x must be non-negative since the square root equals 2*x

(√(,x2+1))2=(2*x)2

x2+1=4*x2

5. Solve for x by isolating the variable.

1=3*x2

x2=1/3

x=±√(,1/3)

6. Check for extraneous solutions by verifying which value satisfies the condition 2*x≥0 from step 3.

x=1/√(,3)

x=√(,3)/3

Final Answer

x-intercept: *(√(,3)/3,0), y-intercept: *(0,−1)

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