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Anna11 [10]
2 years ago
11

11. What is the domain of the function? Please show how you solved it and explain.

Mathematics
1 answer:
joja [24]2 years ago
8 0

Answer:

domain:  x\leq -7, x\geq 3

Step-by-step explanation:

f(x)=\sqrt{x^2+4x-21}

Factor x^2+4x-21:

x^2+4x-21=(x-3)(x+7)

Therefore,

f(x)=\sqrt{(x-3)(x+7)}

\implies f(x)=\sqrt{(x-3)}\sqrt{(x+7)}

Find non-negative values for radicals:

\sqrt{(x-3)} \implies x\geq 3

\sqrt{(x+7)} \implies x\leq -7

Therefore, domain:  x\leq -7, x\geq 3

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Step-by-step explanation:

<em>Solving for the y-intercept:</em>

Since the equation 'y=3/4x - 6' is in the 'y=mx + c' form (where m is the slope and c is the y-intercept):

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<em>Solving for the x-intercept:</em>

When the line intersects with the x-axis, the y-value is 0. Hence, the coordinate is (x,0). Substituting this into 'y=3/4x - 6':

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the x-intercept is (8,0)

<em>Hope this helps and be sure to have a wonderful time ahead at Brainly! :D</em>

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