Trigonometry Examples

Find the Intersection of the Functions f(x) = square root of x+1 , f(x) = square root of x-6
,
Step 1
Substitute for .
Step 2
Solve for .
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Step 2.1
To remove the radical on the left side of the equation, square both sides of the equation.
Step 2.2
Simplify each side of the equation.
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Step 2.2.1
Use to rewrite as .
Step 2.2.2
Simplify the left side.
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Step 2.2.2.1
Simplify .
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Step 2.2.2.1.1
Multiply the exponents in .
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Step 2.2.2.1.1.1
Apply the power rule and multiply exponents, .
Step 2.2.2.1.1.2
Cancel the common factor of .
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Step 2.2.2.1.1.2.1
Cancel the common factor.
Step 2.2.2.1.1.2.2
Rewrite the expression.
Step 2.2.2.1.2
Simplify.
Step 2.2.3
Simplify the right side.
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Step 2.2.3.1
Rewrite as .
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Step 2.2.3.1.1
Use to rewrite as .
Step 2.2.3.1.2
Apply the power rule and multiply exponents, .
Step 2.2.3.1.3
Combine and .
Step 2.2.3.1.4
Cancel the common factor of .
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Step 2.2.3.1.4.1
Cancel the common factor.
Step 2.2.3.1.4.2
Rewrite the expression.
Step 2.2.3.1.5
Simplify.
Step 2.3
Solve for .
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Step 2.3.1
Move all terms containing to the left side of the equation.
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Step 2.3.1.1
Subtract from both sides of the equation.
Step 2.3.1.2
Combine the opposite terms in .
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Step 2.3.1.2.1
Subtract from .
Step 2.3.1.2.2
Subtract from .
Step 2.3.2
Since , there are no solutions.
No solution
No solution
No solution