Question # 01: 05
Find the equation for circle with center (1,3) that passes through (4, -1).
Sol.
Radius of circle r is the distance between (4, -1) and (1, 3)
Question # 02: 05
Given that . Find . Also find the domains of the composite functions.
Sol.
fog(x) = f ( g(x) )
= ( g(x) )2 – 4
= x-2- 4
= x-6
gof(x) = g( f(x) )
Question # 03: 05
Find . (Use rationalization technique to simplify)
Hint: (How to rationalize)
Rationalize the numerator of the expression .
Step I: find the conjugate of the numerator which is and vice versa.
Step II: multiply the numerator and the denominator of the expression with the conjugate
Step III: make sure all the radicals are simplified
Step IV: simplify the fraction if needed.
In the same manner we can rationalize denominator too.
Sol.
Find the equation for circle with center (1,3) that passes through (4, -1).
Sol.
Radius of circle r is the distance between (4, -1) and (1, 3)
Question # 02: 05
Given that . Find . Also find the domains of the composite functions.
Sol.
fog(x) = f ( g(x) )
= ( g(x) )2 – 4
= x-2- 4
= x-6
gof(x) = g( f(x) )
Question # 03: 05
Find . (Use rationalization technique to simplify)
Hint: (How to rationalize)
Rationalize the numerator of the expression .
Step I: find the conjugate of the numerator which is and vice versa.
Step II: multiply the numerator and the denominator of the expression with the conjugate
Step III: make sure all the radicals are simplified
Step IV: simplify the fraction if needed.
In the same manner we can rationalize denominator too.
Sol.
