Odd Neither Describe the transformation from the parent func

Odd Neither Describe the transformation from the parent function y = x^3. y = (x - 4)^3 + 16 4 units to the right and 16 units down 4 units to the right and 16 units up 4 units to the left and 16 units down 4 units to the left and 16 units up State whether true or false. The following functions are inverses of each other. f(x) = -5x + 19 and g(x) = True False Find the equation for the inverse function, f^-1(x). f(x) = x + 3/8 f^-1(x) = -8x - 8 f^-1(x) = 8x - 3 f^-1(x) = -1/3x + 7 f^-1(x) = 1/3x + 7

Solution

38)

y = (x - 4)³ + 16 parent function y= x³

since it has the term \"x-4\" which means we have to shift 4 units towards right

\" x-a \" shift the graph a - units towards right

since it also has \"+16\" ouside the bracket of x term therefore we need to shift 16 units upwards

b) option

39)

f(x) =   -5x +19                ,    g(x) = (x-19) / 5

we need to check whether these function are inverse of each other

we need to finf fog(x) and gof(x)

fog(x) means we substitute g(x) in place of \"x\"

fog(x) = (-5(x-19) / 5) + 19

= (-1(x-19) ) +19                     //            cancel \'5\'

    = -x + 19 + 19                   //     -(x)   = -x   // whenever there is negative sign before a bracket we reverse the sign

   = -x

gof(x) = (-5x + 19 -19) / 5

    = -5x/5

= -x

therefore they are inverse of each other

40)

f(x) = (x+3) / 8

y = (x + 3) / 8

x = (y + 3) / 8           // switch x and y

solve for y

8x = (y+3)                // multiply 8 on both sides

8x - 3 = y

y = 8x - 3

replace y with f^-1(x)

f^-1(x) = 8x - 3