Use the graphs of y fx and y gx to evaluate the function G

Use the graphs of y = f(x) and y = g(x) to evaluate the function. Graphical Reasoning In Exercises 89-92, (a) use a Graphical Reasoning graphing utility to graph the function, (b) use the draw inverse feature of the graphing utility to draw the inverse of the function, and (c) determine whether the graph of the inverse relation is an inverse function, reasoning. f(x) = x^3 + x + 1 g(x) = 3x^2/x^2 + 1 h(x) = x Squareroot 4 - x^2 f(x) = 4x/Squareroot x^2 + 15

Solution

ANSWER Q. 80. See the value of y at -3, -2, 0 and 6 then look at the corresponding value of x. These are the values of f^-1(x). The solution for f^-1(x) are shown in table. below.

Directions: For problems 81 - 88 use the procedure discussed in Question No. 80.

ANSWER Q. 81. f^-1(0) = 0.5 [See the graph of y = f(x) for the value of x at y=0]

ANSWER Q. 82. g^-1(0) = -2 [See the graph of y = g(x) for the value of x at y=0]

ANSWER Q. 83. (fog)(2) = f [g(2)] = f(3) [Since, g(2)=3]

= -2 [From the graph of y=f(x)]

ANSWER Q. 84. g(f(-4)) = g (4) [Since, f(-4)=4]

= 6 [From the graph of y=g(x)]

ANSWER Q. 85. f^-1(g(0)) = f^-1 (2) [Since, g(0)=2]

= 0 [From the graph of y=f(x)]

ANSWER Q. 86. (g^-1of)(3)) = g^-1(f (3)) = g^-1(-2) [Since, f(3)=-2]

= -3 [From the graph of y=g(x)]

ANSWER Q. 87. (gof^-1)(2)) = g (f^-1(2)) =g(0) [Since, f^-1(2)=0]

= 2 [From the graph of y=g(x)]

ANSWER Q. 88. (f^-1og^-1)(-2)) = f^-1(g^-1 (-2) ) = f^-1(-3) [Since, g^-1(-2)=-3]

= 1 [From the graph of y=f(x)]

x (for variable y)	f-1(x)
-3	4
-2	3
0	-1
6	-2