4. if ( f(x)=-\frac{1}{2}x + 6 ), then which of the following values solves the equation ( f(x)=10 )?\n(1)…

4. if ( f(x)=-\frac{1}{2}x + 6 ), then which of the following values solves the equation ( f(x)=10 )?\n(1) 1\n(2) 11\n(3) -8\n(4) -4\n5. the function ( f(x) ) is defined by the formula ( f(x)=x^{2}+2 ) and the function ( g(x) ) is defined by the graph shown below. which of the following is the value of ( f(g(2)) )?\n(1) 18\n(2) 14\n(3) 5\n(4) 9\n6. which of the following values of ( x ) would not be in the domain of the function ( f(x)=\frac{x - 7}{x + 5} )?\n(1) ( x=-5 )\n(2) ( x = 5 )\n(3) ( x=-7 )\n(4) ( x = 7 )\n7. if the point ( (4,-2) ) lies on the graph of the one - to - one function ( f(x) ), then which of the following points must lie on the graph of its inverse function, ( f^{-1}(x) )?\n(1) ( (4,2) )\n(3) ( (-4,2) )\n(2) ( left(\frac{1}{4},-\frac{1}{2}\right) )\n(4) ( (-2,4) )\n9. if ( f(x)=|x - 5| ), then which of the following is the average rate of change of ( f(x) ) over the interval ( 2leq xleq12 )?\n(1) 1\n(2) 0.4\n(3) -1.25\n(4) 0.75

4. if ( f(x)=-\frac{1}{2}x + 6 ), then which of the following values solves the equation ( f(x)=10 )?\n(1) 1\n(2) 11\n(3) -8\n(4) -4\n5. the function ( f(x) ) is defined by the formula ( f(x)=x^{2}+2 ) and the function ( g(x) ) is defined by the graph shown below. which of the following is the value of ( f(g(2)) )?\n(1) 18\n(2) 14\n(3) 5\n(4) 9\n6. which of the following values of ( x ) would not be in the domain of the function ( f(x)=\frac{x - 7}{x + 5} )?\n(1) ( x=-5 )\n(2) ( x = 5 )\n(3) ( x=-7 )\n(4) ( x = 7 )\n7. if the point ( (4,-2) ) lies on the graph of the one - to - one function ( f(x) ), then which of the following points must lie on the graph of its inverse function, ( f^{-1}(x) )?\n(1) ( (4,2) )\n(3) ( (-4,2) )\n(2) ( left(\frac{1}{4},-\frac{1}{2}\right) )\n(4) ( (-2,4) )\n9. if ( f(x)=|x - 5| ), then which of the following is the average rate of change of ( f(x) ) over the interval ( 2leq xleq12 )?\n(1) 1\n(2) 0.4\n(3) -1.25\n(4) 0.75

Answer

Explanation:

Step1: Find (g(2))

From the graph of (g(x)), when (x = 2), (g(2)=3)

Step2: Calculate (f(g(2)))

Since (f(x)=x^{2}+2) and (g(2) = 3), substitute (x = 3) into (f(x)) (f(3)=3^{2}+2=9 + 2=11)

Answer:

(1) (18) (Incorrect) (2) (14) (Incorrect) (3) (5) (Incorrect) (4) (9) (Incorrect)

Explanation:

Step1: Recall the formula for the average rate of change

The average rate of change of a function (y = f(x)) over the interval ([a,b]) is (\frac{f(b)-f(a)}{b - a}) Here, (a = 2), (b=12) and (f(x)=\vert x - 5\vert)

Step2: Calculate (f(2)) and (f(12))

(f(2)=\vert2 - 5\vert=\vert-3\vert = 3) (f(12)=\vert12 - 5\vert=\vert7\vert = 7)

Step3: Calculate the average rate of change

(\frac{f(12)-f(2)}{12 - 2}=\frac{7-3}{10}=\frac{4}{10}=0.4)

Answer:

(1) (1) (Incorrect) (2) (0.4) (Correct) (3) (-1.25) (Incorrect) (4) (0.75) (Incorrect)

Explanation:

Step1: Recall the property of inverse functions

If ((a,b)) lies on the graph of (y = f(x)), then ((b,a)) lies on the graph of (y = f^{-1}(x))

Step2: Apply the property

Given the point ((4,-2)) on (y = f(x)), for the inverse function (y = f^{-1}(x)), the point ((-2,4)) must lie on its graph

Answer:

(1) ((4,2)) (Incorrect) (2) (\left(\frac{1}{4},-\frac{1}{2}\right)) (Incorrect) (3) ((-4,2)) (Incorrect) (4) ((-2,4)) (Correct)

Explanation:

Step1: Recall the domain of a rational function

The domain of a rational function (y=\frac{u(x)}{v(x)}) is all real numbers (x) such that (v(x)\neq0) For (f(x)=\frac{x - 7}{x + 5}), set (x+5\neq0)

Step2: Solve for (x)

(x+5\neq0\Rightarrow x\neq - 5)

Answer:

(1) (x=-5) (Correct) (2) (x = 5) (Incorrect) (3) (x=-7) (Incorrect) (4) (x = 7) (Incorrect)

Explanation:

Step1: Set up the equation

Given (f(x)=-\frac{1}{2}x + 6) and (f(x)=10) So, (-\frac{1}{2}x+6 = 10)

Step2: Solve for (x)

Subtract (6) from both sides: (-\frac{1}{2}x=10 - 6=4) Multiply both sides by (-2): (x=-8)

Answer:

(1) (1) (Incorrect) (2) (11) (Incorrect) (3) (-8) (Correct) (4) (-4) (Incorrect)