ANSWER
EXPLANATION
The given radical expression is
Recall and use
to obtain;
Simplify the second radicand.
We have two like surds so we can simplify to obtain;
Which function has the smallest minimum? (5 points)
1 answer:
f(x) has the smallest minimum. The minimum value of f(x) is -3
The largest sin(x) can get is 1.
This applies to sin(2x-pi) as well. So f(x) is as small as -5*(1)+2 = -5+2 = -3.
You can see this each time the red curve bottoms out at y = -3.
The smallest that g(x) can get is y = -2 as shown at the vertex (3,-2)
The smallest that h(x) can get is y = 3 as shown by the point (1,3)
See the attachment for a visual comparison of the three functions.
The largest sin(x) can get is 1.
This applies to sin(2x-pi) as well. So f(x) is as small as -5*(1)+2 = -5+2 = -3.
You can see this each time the red curve bottoms out at y = -3.
The smallest that g(x) can get is y = -2 as shown at the vertex (3,-2)
The smallest that h(x) can get is y = 3 as shown by the point (1,3)
See the attachment for a visual comparison of the three functions.
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Start with
We observe that both fractions are not defined if . So, we will assume
.
We multiply both numerator and denominator of the first fraction by 3 and we sum the two fractions:
We multiply both sides by :
We move everything to one side and solve the quadratic equation:
We check the solution:
which is true